Answer to Question #202091 in Optics for Prachi

Question

Interference fringes are produced by a beam of monochromatic light incident normally on a wedge shaped film of refractive index 1.5. The angle of the wedge is 15 seconds of an arc and the two successive dark fringes are 0.4 cm apart. Calculate the wavelength of light.

Answer 1

 path difference $= n . \lambda$ = $d sin \theta$

where $n$  is its index of refraction

$\therefore$ n =1.5

path diiference $=0.4 cm (0.4$ $×10$ ^-2$m)$

$\lambda$ $=?$

$\therefore$ path difference $=n.\lambda$

$10$ ^-2$× 0.4 = (1.5 × \lambda$ $)$

$\lambda = ( 0.4 × 10$ ^-2$)$ $÷ 1.5$

answer $\lambda = 2. 667 ×10$ ^-3 $m$