EXHIBIT 5.1

            [Kaye, Scholer, Fierman, Hays & Handler, LLP Letterhead]

                                                                   April 3, 2000

Veeco Instruments Inc.
Terminal Drive
Plainview, New York 11803

Gentlemen:

    We have acted as counsel to Veeco Instruments Inc. (the "Company"), in
connection with its registration statement on Form S-4 (the "Registration
Statement") filed pursuant to the Securities Act of 1933, as amended (File No.
333-32608), relating to the proposed offering of up to 6,000,000 shares of its
common stock, par value $0.01 per share (the "Shares"), to be issued to
stockholders of CVC, Inc. ("CVC") in connection with the merger of a
wholly-owned subsidiary of the Company with CVC (the "Merger").

    In that connection, we have reviewed the certificate of incorporation of the
Company, its by-laws, resolutions adopted by its Board of Directors, the
Registration Statement, and such other documents and proceedings as we have
deemed appropriate.

    On the basis of such review, and having regard to such factual and legal
considerations that we deem relevant, we are of the opinion that:

    The Shares to be issued by the Company in the Merger have been duly
authorized and, when issued in accordance with the terms set forth in the
Registration Statement, will be duly and validly issued, fully paid and
nonassessable.

    We hereby consent to the use of our name under the caption "Legal Matters"
in the joint proxy statement/prospectus included in the Registration Statement
and to the filing of this opinion as an exhibit to the Registration Statement.

                                          Very truly yours,

                                          /s/ Kaye, Scholer, Fierman, Hays &
                                          Handler, LLP