(a) How many bright rings are produced? Assume that ? = 569 nm. 1 rings (b) How

Question

    (a) How many bright rings are produced? Assume that ? = 569 nm.
1      rings

    (b) How many bright rings would be produced if the arrangement were immersed in water (n = 1.33)?
2      rings The figure below shows a lens with radius of curvature R lying on a flat glass plate and illuminated from above by light with wavelength ?. This photo, taken from above the lens, shows that circular interference fringes (called "Newton's rings") appear, associated with the variable thickness d of the air film between the lens and the plate. The radius of curvature R of the lens is 5.0 m and the lens diameter is 15 mm. (Ignore the interference between the top and bottom surfaces of the lens.) How many bright rings are produced? Assume that ? = 569 nm. How many bright rings would be produced if the arrangement were immersed in water (n = 1.33)?

Explanation / Answer

?a beam reaching the air gap will split into beam_1 reflecting from the gap back into the lens, and beam_2 that enters the gap, reflects from the flat plate back into the air gap, and exits from the gap back into the lens;

?optical path of beam_2 is longer than that of beam_1 by

?s=2t, where t is the size across the gap;

?to see a bright ring we must admit that

?s = (2k +1) ?/2, where ?=569e-9 m, integer k=0,1,2,3, etc;

Thus 2t =(2k +1) ?/2, where t=1.5e-5m is max size across the gap;

Therefore 2k +1 = round(105.4) =105, hence k =53;

including k=0 we get

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.