Question 286: Dual Nature of Matter and Radiation

Question

A parallel beam of light is incident normally on a plane surface absorbing $50 \%$ of the light and reflecting the rest. If the incident beam carries 90 W of power, the force exerted by it on the surface is ( $\mathrm{C}=$ velocity of light in air $=3 	imes 10^8 \mathrm{~m} / \mathrm{s}$ )

Accepted Answer

Given:
Power of incident light, $P = 90$ W
Surface absorbs $50\%$ of the light and reflects $50\%$
Speed of light, $c = 3 	imes 10^8$ m/s
Let's follow the
NCERT method
:
Step 1:
Find the force due to absorption
When light is
absorbed
, the force exerted on the surface is:
$$ F_{	ext{abs}} = \frac{P_{	ext{absorbed}}}{c} $$
Since $50\%$ is absorbed:
$$ P_{	ext{absorbed}} = 0.5 	imes 90 = 45~	ext{W} $$
So,
$$ F_{	ext{abs}} = \frac{45}{3 	imes 10^8} = 1.5 	imes 10^{-7}~	ext{N} $$
Step 2:
Find the force due to reflection
When light is
reflected normally
(for normal incidence and perfect reflection), the change in momentum is
twice
that of absorption.
Force due to
reflection
:
$$ F_{	ext{ref}} = \frac{2P_{	ext{reflected}}}{c} $$
Since $50\%$ is reflected:
$$ P_{	ext{reflected}} = 0.5 	imes 90 = 45~	ext{W} $$
Thus,
$$ F_{	ext{ref}} = \frac{2 	imes 45}{3 	imes 10^8} = \frac{90}{3 	imes 10^8} = 3 	imes 10^{-7}~	ext{N} $$
Step 3:
Total force exerted
$$ F_{	ext{total}} = F_{	ext{abs}} + F_{	ext{ref}} $$
$$ F_{	ext{total}} = 1.5 	imes 10^{-7}~	ext{N} + 3 	imes 10^{-7}~	ext{N} $$
$$ F_{	ext{total}} = 4.5 	imes 10^{-7}~	ext{N} $$
Correct answer:
$\boxed{4.5 	imes 10^{-7}~	ext{N}}$ (Option A)

Answer

$4.5 	imes 10^{-7} \mathrm{~N}$

Answer

$1.5 	imes 10^{-7} \mathrm{~N}$

Answer

$3 	imes 10^{-7} \mathrm{~N}$

Answer

$9 	imes 10^{-7} \mathrm{~N}$

Dual Nature of Matter and Radiation

A parallel beam of light is incident normally on a plane surface absorbing 50 \% of the light and reflecting the rest. If the incident beam carries 90 W of power, the force exerted by it on the surface is ( \mathrm{C}= velocity of light in air =3 \times 10^8 \mathrm{~m} / \mathrm{s} )

Choose the correct answer: