EXHIBIT 5.1 [KAYE SCHOLER LLP LETTERHEAD] (212) 836-8000 September 17, 2001 Veeco Instruments Inc. 100 Sunnyside Boulevard Woodbury, New York 11797 Ladies and Gentlemen: We have acted as special counsel to Veeco Instruments Inc., a Delaware corporation (the "Company"), in connection with the Company's registration statement on Form S-8 (the "Registration Statement") to be filed pursuant to the Securities Act of 1933, as amended. The Registration Statement relates to an aggregate of 809,642 shares of the Company's common stock, par value $.01 per share (the "Common Stock"), (a) 431,537 of which may be issued upon the exercise of stock options granted pursuant to the Applied Epi, Inc. 1993 Stock Option Plan, (b) 72,678 of which may be issued upon the exercise of stock options granted pursuant to the Applied Epi, Inc. 2000 Stock Option Plan and (c) 305,427 of which may be issued upon the exercise of stock options granted pursuant to non-qualified restricted stock option agreements between Applied Epi, Inc. and certain employees and former employees of Applied Epi, Inc. The Applied Epi, Inc. option plans and stock option agreements described in clauses (a) through (c) above are referred to in this opinion collectively as the "Option Plans". The Option Plans have been assumed by the Company pursuant to the terms of the Agreement and Plan of Merger (the "Merger Agreement") among the Company, Veeco Acquisition Corp., Applied Epi, Inc., the shareholders of Applied Epi, Inc. listed on the signature pages thereto and Paul E. Colombo, as Stockholders' Representative, dated as of September 6, 2001, whereby Veeco Acquisition Corp., a wholly-owned subsidiary of Veeco, merged with and into Applied Epi, Inc. (the "Merger"). The Merger was consummated on September 17, 2001. In that connection, we have reviewed the Company's Amended and Restated Certificate of Incorporation, as amended, its Third Amended and Restated Bylaws, resolutions adopted by its Board of Directors and its stockholders, the Registration Statement, the Option Plans, the Merger Agreement and such other documents and proceedings as we have deemed appropriate. On the basis of such review, and having regard to legal considerations that we deem relevant, we are of the opinion that, assuming the due authorization and valid issuance of the options being assumed by Veeco in the Merger under the Option Plans, the shares of Common Stock to be offered pursuant to the Registration Statement have been duly authorized and, when issued in accordance with the terms set forth in the Option Plans, will be validly issued, fully paid and nonassessable. We advise you that we are members only of the Bar of the State of New York and that our opinion set forth above is based as to matters of law solely on applicable provisions of the General Corporation Law of the state of Delaware, and we express no opinions as to any other laws, statutes, ordinances, rules or regulations. 10 We hereby consent to the filing of this opinion as an exhibit to the Registration Statement. In giving this opinion, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Securities and Exchange Commission. Very truly yours, /s/ Kaye Scholer LLP 11