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PhysicsNumerical+3Question 13 of 54

JEE Advanced 2018 · Paper 1, Physics question 13

Sunlight of intensity 1.3 kW m−21.3\ \mathrm{kW\,m^{-2}} is incident normally on a thin convex lens of focal length 20 cm. 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 kW m−2\mathrm{kW\,m^{-2}}, at a distance 22 cm from the lens on the other side is ______.

Answer and worked solution

Official answer: 130

Parallel light converges to the focus at 20 cm and then spreads out. At 22 cm it is 2 cm past the focus.

Beam size. By similar triangles, the beam diameter there is 220=110\dfrac{2}{20}=\dfrac1{10} of the lens aperture, so its area is 1100\dfrac1{100} as large.

Intensity. All the power passes through:
I=1.3×100=130 kW m−2.I=1.3\times100=130\ \mathrm{kW\,m^{-2}}.

Answer: 130

Topics:Thin lenses and lens maker's formulaEnergy and momentum of EM waves
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