devarshi-dt-logo

Question:

Sunlight of intensity 1.3 kW/m² 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/m², at a distance 22 cm from the lens on the other side is _____.

Solution:

r/R = 22/20 = 11/10
∴ Ratio of area = (r/R)² = 121/100
Let energy incident on lens be E.
∴ Given E/A = 1.3
To calculate: final E/a
E/a = A × 1.3/a
Also A/a = 121/100
∴ Average intensity of light at 22 cm = E/a = A × 1.3/a = 100/121 × 1.3 = 130/121 kW/m² ≈ 1.07 kW/m²