Question

Dipping the frame in a soap solution forms a rectangle film of length l = 0.02 m and height h = 0.030 m. White light falls on the film at an angle a = 30º (measured with respect to the normal direction). The reflected light displays a green colour of wavelength l₀ (500 nm). If density of soap = 1000 kg m^–3, then find the mass of the thinnest film? (m_soap = 1.33)

• A. 0.18 mg
• B. 0.30 mg
• C. 0.06 mg
• D. 0.01 mg

Answer 1

Answer: (C)

0.06 mg

Answer 2

2$\mu t$cos r = (2n + 1) $\frac{\lambda}{2}$

$t = \frac{(2n + 1)\lambda}{4\mu\cos r}$ (putting n 0)

= $\frac{\lambda}{4\mu\cos r}$

cos r = $\sqrt{1 - \sin^{2}r}$ = $\frac { 1 } { \mu }$ $\sqrt{\mu^{2} - \sin^{2}\beta}$

Substituting all value t = 1.01 × 10^–7m

mass of soap = r × l × h × t = 6.06 × 10^–2 mg