A Newton’s-ring apparatus consists of a glass lens with radius of curvature R that rests on a flat glass plate as shown in Figure. The thin film is air of variable thickness. The pattern is viewed by reflected light.

(a) Show that for a thickness t the condition for a bright (constructive) interference ring is

(b) Apply the Pythagorean theorem to the triangle of sides r, R – t, and hypotenuse R to show that for t << R, the radius of a fringe is related to t by

r = √2tR

(c) How would the transmitted pattern look in comparison with the reflected one?
(d) Use R = 10 m and a diameter of 4 cm for the lens. How many bright fringes would you see if the apparatus were illuminated by yellow sodium light (λ ≈ 590 nm) and were viewed by reflection? 

(e) What would be the diameter of the sixth bright fringe?
(f) If the glass used in the apparatus has an index of refraction n = 1.5 and water (nW = 1.33) is placed between the two pieces of glass, what change will take place in the bright fringes?

Transcribed Image Text:

R п 72