Question

A surface of a glass plate is covered with a thin layer of water. A light with wavelength = 0.680 mm incident at an angle of 30⁰. Due to evaporation of the water layer, the intensity of the reflected light change periodically. Time interval between the appearances of maximum intensity is equal to 15.0 minutes. Find the rate of decrease of the water layer thickness. (m_g = 1.50 and m_w = 1.34)

• A. 4.01 mm/hr
• B. 1.01 mm/hr
• C. 6.01mm/hr
• D. 12.01 mm/hr

Answer 1

Answer: (B)

1.01 mm/hr

Answer 2

Condition for constructive interference

2mt cos r = nl

sin 30⁰ = 1.34 sin r

sin r = $\frac { 1 } { 3 }$

cos r =

2 mt cos r = nl ... (1)

2 m(t _ Dt) cos r = (n _ 1)l .. (2)

Equation (1) and equation (2)

By eq.(1) and eq.(2)

2m Dt cos r = l

Dt = $\frac { \lambda } { 2 \mu \cos r }$

Rate of decrease = ₌ 1.01 mm/hr

[Time = 15 min = $\frac { 15 } { 60 }$hr]