JEE Advanced · 2018 · 20 May 2018 · Paper 1 · Geometrical Optics

Sunlight of intensity

1.3 k W m^{- 2}

is incident normally on a thin convex lens of focal length

20 c m

. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in

k W m^{- 2}

, at a distance

22 c m

from the lens on the other side is ____.

Answer: 130

Solution

The lens focuses parallel rays to a point at the focal length. At distance 22 cm (2 cm beyond focus), the beam has spread. Using similar triangles and the small aperture approximation: the area ratio is

(20/2)^{2} = 100

. By energy conservation,

I_{1} A_{1} = I_{2} A_{2}

, so

I_{2} = I_{1} \times 100 = 1.3 \times 100 = 130

kW/m².

JEE Advanced · 2018 · 20 May 2018 · Paper 1 · Numerical answer

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