A totally reflecting, small plane mirror placed horizontally faces a parallel beam of light as shown in the fig. The mass of the mirror is 20 g. Assume that there is no absorption in the lens and that 30% of the light emitted by the source goes through the lens. Find the power (in $\times 10^{8} W)$ of the source needed to support the weight of the mirror. Take $g = 10 m s^{- 2}$ .

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Solution

Weight of lens $= 20 \times 10 = 200 g \times m - s^{- 2}$

Effective % of light photons from source balancing the lens weight $= 70 - 30 = 40 %$

Hence, $200 = \frac{40}{100} \times \frac{h}{λ}$

Simplifying and multiplying by c on both sides, we get:

$1.5 \times 10^{8} W = \frac{h c}{λ}$

$∴$ Power in $10^{8} W = 1.5$

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Which of the following can make a parallel beam of light when light from a point source is incident on it?

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(d) Concave mirror as well as concave lens

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Weight of lens =20×10=200g×m−s−2Effective % of light photons from source balancing the lens weight =70−30=40%Hence, 200=40100×hλ Simplifying and multiplying by c on both sides, we get:1.5×108W=hcλ∴ Power in 108W=1.5