Question

A puddle of water has a thin film of gasoline floating on it. A beam of light is shining perpendicular on the film. If the wavelength of light incident on the film is 560 nm and the indices of refraction of gasoline and water are 1.40 and 1.33, respectively, what must be the minimum thickness of the film to see a bright reflection? 100 nm 200 nm 300 nm 400 nm 500 nm

Answer 1

Answer:

option A

Explanation:

Given,

wavelength of light,$\lambda = 560\ nm$

refractive index of gasoline, n₁ = 1.40

Refractive index of water, n₂ = 1.33

thickness of the film, t = ?

Condition of constructive interference is given by

$2 n t = (m+\dfrac{1}{2})\lambda$

For minimum thickness of the film m = 0

From the question we can clearly observe that phase change from gasoline to air

so, n = 1.4

$2 \times 1.4 \times t = \dfrac{560}{2}$

$t = 100\ nm$

Hence, the correct answer is option A