<PAGE>   1
                                                                    EXHIBIT 10.4

                                                      Adopted: 20 September 2000
                                                      Approved: 10 November 2000


                             SYNAPTICS INCORPORATED

                        2000 UK APPROVED SUB-PLAN TO THE
                  SYNAPTICS INCORPORATED 1996 STOCK OPTION PLAN

In pursuance of its powers under the Synaptics Incorporated 1996 Stock Option
Plan ("the Plan"), the Board of Directors, or a duly appointed committee of the
Board of Directors of Synaptics Incorporated ("the Company") has adopted these
rules for the purposes of operating the Plan with regard to such options which
these rules are expressed to extend at the time when the option is granted.
Unless the context requires otherwise, all expressions used in these rules have
the same meaning as the Plan. The Plan, as supplemented by these rules, is
referred to hereinafter as "the Sub-Plan". For the avoidance of doubt, the terms
of the Plan (insofar as they have not been disapplied by Rule 14 of these rules)
shall form part of the Sub-Plan.

1.       The shares of Common Stock over which options may be granted under the
         Sub-Plan form part of the ordinary share capital (as defined in section
         832(1) Income and Corporation Taxes Act 1988) (ICTA 1988) of the
         Company and must at all times, including the time of grant and the time
         of exercise, comply with the terms of the Plan and comply with the
         requirements of paragraphs 10 - 14 Schedule 9 ICTA 1988.

2.       The companies participating in this Sub-Plan are the Company and all
         companies controlled by the Company within the meaning of Section 840
         ICTA 1988 ("the Subsidiaries") and which have been nominated by the
         Company to participate for the time being in this Sub-Plan.

3.       The shares of Common Stock to be acquired on exercise of the option in
         accordance with the terms of the Sub-Plan will:

         (a)      be fully paid up;

         (b)      be not redeemable;

         (c)      not be subject to any restrictions other than restrictions
                  which attach to all shares of stock of the same class. For the
                  purpose of this clause, the term restrictions includes
                  restrictions which are deemed to attach to the shares under
                  any contract, agreement, arrangement or condition as referred
                  to in paragraph 13 Schedule 9 ICTA 1988.

4.       Synaptics Incorporated has only one class of shares of Common Stock,
         and only the Common Stock is ordinary share capital as defined under
         section 832(1) ICTA 1988.

5.       No option will be granted to an employee or director under this
         Sub-Plan, or where an option has previously been granted no option
         shall be exercised by an option-holder if at that time he has, or any
         time within the preceding 12 months has had, a material interest for
         the purposes of Schedule 9 ICTA 1988 in either the Company being a
         close
<PAGE>   2
         company (within the meaning of Chapter I of Part XI of ICTA 1988) or in
         a company being a close company which has control (within the meaning
         of section 840 ICTA 1988) of the Company or in a company being a close
         company and a member of a consortium (as defined in section 187(7) ICTA
         1988) which owns the Company. In determining whether a company is a
         close company for this purpose section 414(1)(a) ICTA 1988 (exclusion
         of companies not resident in the United Kingdom) and section 415 of
         ICTA 1988 (exclusion of certain companies with listed shares) shall be
         disregarded.

6.       Notwithstanding the provisions of Section 8 of the Plan, no option will
         be granted to an employee or director under this Sub-Plan in relation
         to which the exercise price is manifestly less than the market value
         (as defined in section 187(2) ICTA 1988) of the Company's shares of
         Common Stock on the date of grant of the option mad the exercise price
         shall be stated at the date of the option grant. The market value is to
         be agreed in accordance with the provisions of Part VIII of the
         Taxation of Chargeable Gains Act 1992 and agreed for the purposes of
         the Scheme with the Inland Revenue Shares Valuation Division at the
         date of grant.

7.       (a)      Notwithstanding the provisions of Section 14 of the Plan, any
                  alteration or amendment to the Plan or this Sub-Plan which
                  affects the Sub-Plan shall not have effect until approved by
                  the Board of Inland Revenue. The Company undertakes to provide
                  details thereof to the Board of Inland Revenue without delay
                  for this purpose.

         (b)      Notwithstanding the provisions of Section 11 no adjustment
                  pursuant to any of the provisions of the Plan shall be made to
                  any option which has been granted under the Sub-Plan unless
                  such adjustment would be permitted under the Plan and under
                  the provisions of paragraph 29 of Schedule 9 ICTA 1988 and is
                  necessary to take account of any variation in the share
                  capital of which the Common Stock forms part and where so
                  permitted no such adjustment shall take effect until the
                  approval of the Board of Inland Revenue shall have been
                  obtained thereto.

8.       Notwithstanding anything contained in Section 11 of the Plan, if the
         Company merges or is consolidated with another company under
         circumstances where the Company is not the surviving company, no
         options may be granted under this Sub-Plan following such merger, or
         consolidation.

9.       For the avoidance of doubt it is stated that the Company is the grantor
         as defined in paragraph 1(1) Schedule 9 ICTA 1988.

10.      Any option granted to an employee or director under this Sub-Plan shall
         be limited to take effect so that immediately following such grant the
         aggregate market value (determined at the time prescribed by paragraph
         28 Schedule 9 ICTA 1988 and calculated in accordance with the
         provisions of the said Schedule 9) of shares which he can acquire under
         this Sub-Plan and any other plan or plans, not being a savings-related
         share option scheme, approved under the said Schedule 9 and established
         by the grantor or by any associated company (as defined in section 416
         ICTA 1988) of the grantor (and not exercised) shall not exceed L30,000
         or such other sum as may be prescribed from time to


                                       2
<PAGE>   3
         time by paragraph 28 Schedule 9 ICTA 1988. Provided always that this
         limit shall not exceed the limitations set out in the Plan.

11.      An option will only be granted under this Sub-Plan to any employee
         (other than one who is a director) or a full-time director of the
         Company or a company participating in this Sub-Plan. For this purpose,
         a full-time director is one who is required to work at least 25 hours a
         week excluding meal-times in the business of the Company or its
         subsidiaries.

12.      The Company shall not later than 30 days upon actual receipt of the
         written notice of exercise of an option given in accordance with the
         provisions of the Plan together with the payment of the aggregate
         exercise price in respect of the shares of Common Stock to be issued
         pursuant to the exercise of an option, allot and issue credited as
         fully paid to the Optionee and cause to be registered in his name the
         number of shares of Common Stock specified in the written notice.

13.      When the Board under the powers conferred by Section 4(c)(vi) of the
         Plan determines the terms and conditions of any option granted under
         this Sub-Plan, such terms and conditions shall:

         (i)      be objective, specified at the time of grant and set out in
                  full in or details given with the award; and

         (ii)     be such that rights to exercise such options after the
                  fulfillment or attainment of any terms and conditions so
                  specified shall not be dependent upon the further discretion
                  of any person; and

         (iii)    not be capable of amendment, variation or waiver unless an
                  event occurs which causes the Committee to consider that a
                  waived, varied or amended term and condition would be a fairer
                  measure of performance and would be no more difficult to
                  satisfy.

14.1     The following wording in Section 10 shall be deleted and shall
         therefore be disregarded for the purposes of the Sub-Plan. "At the
         discretion of the Administrator, Optionees may satisfy withholding
         obligations as provided in this paragraph. When an Optionee incurs tax
         liability in applicable tax laws, and the Optionee is obligated to pay
         the Company an amount required to be withheld under applicable tax
         laws, the Optionee may satisfy the withholding tax obligation by one or
         some combination of the following methods: (a) by cash payment, or (b)
         out of Optionee's current compensation, (c) if permitted by the
         Administrator, in its discretion, by surrendering to the Company Shares
         that (i) in the case of Shares previously acquired from the Company,
         have been owned by the Optionee for more than six months on the date of
         surrender, and (ii) have a fair market value on the date of surrender
         equal to or less than Optionee's marginal tax rates times the ordinary
         income recognized, or (d) by electing to have the Company withhold from
         the Shares to be issued upon exercise of the Option, if any, that
         number of Shares having a fair market value equal to the amount
         required to be withheld. For this purpose, the fair market value


                                       3
<PAGE>   4
         of the Shares to be withheld shall be determined on the date that the
         amount of tax to be withheld is to be determined (the "Tax Date").

14.2     The above wording is replaced with the following for the purposes of
         the Sub-Plan:

         "The Optionee is obligated to satisfy the withholding obligations as
         provided in this paragraph. When an Optionee incurs tax liability in
         connection with an Option, which tax liability is subject to tax
         withholding under applicable tax laws, the Optionee will satisfy the
         withholding tax obligation by one or some combination of the following
         methods: (a) by cash payment, or (b) out of Optionee's current
         compensation.

15.      The following, namely:

         (a)      all references in the Plan to "Incentive Stock Options;

         (b)      all payment forms in Section 8(b) other than cash, cheque or
                  delivery of a properly executed exercise notice together with
                  such other documentation as the Administrator and the broker,
                  if applicable, shall require to effect an exercise of the
                  Option and delivery to the Company of the sale or loan
                  proceeds required to pay the exercise price and any applicable
                  income or employment taxes;

         (c)      Section 4 (c)(vii) allowing options to be settled in cash;

         (d)      Section 4 (c)(viii) allowing the amendment of the exercise
                  price;

         (e)      Section 4 (c)(x) allowing discretion to modify granted
                  options;

         (f)      Section 9(f) providing for Buyout Provisions;

                  shall be deleted and shall therefore be disregarded for the
                  purposes of the Sub-Plan.

16.      The first sentence of Section 5(a) shall be amended to read as follows:

         "Nonstatutory Stock Options may be granted to Employees."

17.      Section 8 (a)(ii)(B) shall be amended to read as follows:

         "granted to any person, the per Share exercise price shall be no less
         than the market value per Share on the date of grant as agreed in
         advance with the Inland Revenue in accordance with Rule 6 of the
         Sub-Plan."

Adopted on behalf of the Company by:      /s/ Francis Lee
                                    --------------------------------------------
Position of signatory: CEO
                      -------------------------------------------
Date:                  Nov 10, 2000
                      -------------------------------------------


                                       4
<PAGE>   5
                                   APPENDIX IV

                             SYNAPTICS INCORPORATED



                             STOCK OPTION AGREEMENT


                            2000 UK APPROVED SUB-PLAN
                                     to the
                  SYNAPTICS INCORPORATED 1996 STOCK OPTION PLAN


You are granted effective as of .........................., options (the
"Options") to purchase shares of common stock, zero par value, of Synaptics
Incorporated (the "Option Shares") pursuant to the Synaptics Incorporated 1996
Stock Option Plan (the "Plan") of Synaptics Incorporated (the "Company") as
amended by the 2000 UK Approved Sub-Plan referred to hereinafter as the
"Sub-Plan". The Options are subject to the terms and conditions set forth below
and in the Sub-Plan rules, which are attached to and made a part of this Stock
Option Agreement (the "Agreement"). Capitalised terms used in the Agreement have
the same meaning as defined in the Sub-Plan.

1 Exercise Price: $ ............. per Option Share, being the market value of
the stock at the date of the grant.

         (a)   Number of Option Shares: ...........................

         (b)   Exercise:   Options may be exercised at 25% on the twelve (12)
                           month anniversary of the Vesting Commencement Date
                           (as specified below) and 1/48th of the total number
                           of Option Shares on each monthly anniversary
                           thereafter, except in circumstances as defined in the
                           Plan.

         (c)   Vesting Commencement Date  ...........................

2 Exercise of Option: Exercise must be made by delivery to the Company at its
principal executive office of a notice signed by the Optionee that states the
number of shares to be purchased and is accompanied by payment of the Exercise
Price for the shares to be purchased in substantially the form attached hereto
as Exhibit B.

3 Registration under Federal and State Securities Laws: These Options may not be
exercised and the Company is not required to deliver shares of Common Stock
unless such shares have been registered under Federal and applicable state
security laws, or are then exempt from such registration requirements.
<PAGE>   6
4 Transferability of Options: These Options are not transferable except that on
the death of the Optionee, the Option may be transferred to the Optionee's legal
representative and exercised within six months from the date of death.

5 Market Standoff Agreement: In the event of an initial public offering of the
Company's shares and upon the request of the Company (or the underwriters
managing such underwritten offering of the Company's shares), you are obliged
not to sell, make any short sale of, loan, grant any option for the purchase of,
or otherwise dispose of any shares of the Company (other than those included in
the registration) without the prior written consent of the Company or such
underwriters, as the case may be, for such period of time (not to exceed 180
days) from the effective date of such registration as may be requested by the
Company (or such managing underwriters) and to execute an agreement reflecting
the foregoing as may be requested by the underwriters at the time of the
Company's initial public offer.

6 Expiration Date: The Options expire 90 days after termination of employment
except if the Optionee terminates employment by reason of death or total and
permanent disability, when the Option expires six months and twelve months (six
months in the event of a disability that is not total and permanent)
respectively after termination of employment. Subject to earlier termination as
provided in this Agreement, the Options expire on the tenth anniversary of the
date of grant, unless earlier exercised.

7 Taxation: No income tax will be payable when you exercise the Option provided
the Sub-Plan is still approved by the Inland Revenue and:-

  (a)      at least three years and no more than ten years have elapsed
           from the Option Grant Date; and

  (b)      at least three years have elapsed since the date on which you
           last exercised an option obtained under an approved scheme
           (except a savings-related scheme) for which income tax relief
           was given.


The Company by its duly-authorised officer agrees to the Terms and Conditions of
the Agreement and of the Sub-Plan.


SYNAPTICS INCORPORATED




By:
   -------------------------------
<PAGE>   7
The Optionee accepts the Option subject to the terms and conditions of the
Sub-Plan and this Agreement.

   -------------------------------
Optionee
<PAGE>   8
                                   APPENDIX V

                                    EXHIBIT B

                             SYNAPTICS INCORPORATED



                           STOCK OPTION EXERCISE FORM


                            2000 UK APPROVED SUB-PLAN
                                     to the
                  SYNAPTICS INCORPORATED 1996 STOCK OPTION PLAN



Corporate Secretary
Synaptics Incorporated
[Head Office Address]



Dear

I hereby exercise [    ] of my options dated [    ] (the "Shares"), having an
exercise price of $[ ] per share. Attached hereto is a cheque in payment of the
exercise price in the amount of $[    ].

I acknowledge and agree that I shall be required to comply with the attached
schedule detailing the relevant US securities laws for private companies. I
further acknowledge and agree that these are not specific restrictions to
employee shareholders and apply to all shares in the Company.

Thank you for your assistance.


Yours sincerely,


[Purchaser]
<PAGE>   9
US SECURITIES LAWS

1        MARKET STANDOFF AGREEMENT

         In connection with the initial public offering of the Company's
         securities and upon request of the Company or the underwriters managing
         such underwritten offering of the Company's securities, Purchaser
         agrees not to sell, make any short sale of, loan, grant any option for
         the purchase of, or otherwise dispose of any securities of the Company
         (other than those included in the registration) without the prior
         written consent of the Company or such underwriters, as the case may
         be, for such period of time (not to exceed 180 days) from the effective
         date of such registration as may be requested by the Company or such
         managing underwriters and to execute an agreement reflecting the
         foregoing as may be requested by the underwriters at the time of the
         Company's initial public offering.

2        INVESTMENT AND TAXATION REPRESENTATIONS

         In connection with the purchase of the Shares, Purchaser represents to
         the Company the following:

         (a)               Purchaser is aware of the Company's business affairs
                  and financial condition and has acquired sufficient
                  information about the Company to reach an informed and
                  knowledgeable decision to acquire the Shares. Purchaser is
                  purchasing the Shares for investment for his or her own
                  account only and not with a view to, or for resale in
                  connection with, any "distribution" thereof within the meaning
                  of the Securities Act of 1933 (the "Securities Act").

         (b)               Purchaser understands that the Shares have not been
                  registered under the Securities Act by reason of a specific
                  exemption therefrom, which exemptions depends upon, among
                  other things, the bona fide nature of Purchaser's investment
                  intent as expressed herein.

         (c)               Purchaser understands that the Shares are "restricted
                  securities" under applicable US federal and state securities
                  laws and that, pursuant to these laws, Purchaser must hold the
                  Shares indefinitely unless they are registered with the
                  Securities and Exchange Commission and qualified by state
                  authorities, or an exemption from such registration and
                  qualification requirements is available. Purchaser
                  acknowledges that the Company has no obligation to register or
                  qualify the Shares for resale. Purchaser further acknowledges
                  that if an exemption from registration or qualification is
                  available, it may be conditioned on various requirements
                  including, but not limited to, the time and manner of sale,
                  the holding period for the Shares, and requirements relating
                  to the Company which


                                      -2-
<PAGE>   10
                  are outside of the Purchaser's control, and which the Company
                  is under no obligation and may not be able to satisfy.

         (d)               Purchaser understands that Purchaser may suffer
                  adverse tax consequences as a result of Purchaser's purchase
                  or disposition of the Shares. Purchaser represents that
                  Purchaser has consulted any tax consultants Purchaser deems
                  advisable in connection with the purchase or disposition of
                  the Shares and that Purchaser is not relying on the Company
                  for any tax advice.

3        RESTRICTIVE LEGENDS AND STOP-TRANSFER ORDERS

         (a)      LEGENDS           The certificate or certificates representing
                  the Shares shall bear the following legends (as well as any
                  legends required by applicable state and federal corporate and
                  securities laws):

                  (i)               The shares represented by this certificate
                           have not been registered under the Securities Act of
                           1933, and have been acquired for investment and not
                           with a view to, or in connection with, the sale or
                           distribution thereof. No such sale or distribution
                           may be effected without an effective registration
                           statement related thereto or an opinion of counsel in
                           a form satisfactory to the company that such
                           registration is not required under the Securities Act
                           of 1933.

                  (ii)              The shares represented by this certificate
                           may be transferred only in accordance with the terms
                           of tm agreement between the company and the
                           shareholder, a copy of which is on file with the
                           Secretary of the company.

         (b)      STOP-TRANSFER NOTICES      Purchaser agrees that, in order to
                  ensure compliance with the restrictions referred to herein,
                  the Company may issue appropriate "stop transfer" instructions
                  to its transfer agent, if any, and that, if the Company
                  transfers its own securities, it may make appropriate
                  notations to the same effect in its own records.

         (c)      REFUSAL TO TRANSFER        The Company shall not be required
                  (i) to transfer on its books any Shares that have been sold or
                  otherwise transferred in violation of any of the provisions of
                  this Agreement or (ii) to treat as owner of such Shares or to
                  accord the right to vote or pay dividends to any purchaser or
                  other transferee to whom such Shares shall have been so
                  transferred.

         (d)      REMOVAL OF LEGEND          The Shares then held by Purchaser
                  will no longer be subject to the legend referred to in Section
                  3(a)(ii) following the expiration or termination of the market
                  standoff provisions of Section 1 (and of any agreement entered
                  pursuant to Section 1). After such time, and upon Purchaser's
                  request, a new certificate or certificates representing the
                  Shares not repurchased shall be


                                      -3-
<PAGE>   11
                  issued without the legend referred to in Section 3(a)(ii), and
                  delivered to Purchaser.

4        NO EMPLOYMENT RIGHTS

         Nothing in this Agreement shall affect in may manner whatsoever the
         right or power of the Company, or a Parent or Subsidiary of the
         Company, to terminate Purchaser's employment or consulting
         relationship, for any reason, with or without cause.


                                      -4-