Sunlight of intensity `1.3kW 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)`, at a distance 22 cm from the lens on the other side is __________.

Answer

`130.00`

Explanation

From given figure, triangle are similar

`(R )/(20) = (r )/(2) = (1)/(10)`
Let `A_(0)` and `A._(0)` be areas of lens and its image on screen
`(A._(0))/(A_(0)) = ((r )/(R ))^(2) = ((1)/(10))^(2) = (1)/(100)`
`rArr A_(0) = 100 A._(0)`
Power intensity of lens `P_(0) = I_(0)A_(0) = 1.3 A_(0)`
There is no loss of intensity,
so average intensity arrive on the screen is
`I._(0) = (P_(0))/(A._(0)) = (1.3 A_(0))/(A._(0)) = (1.3 xx 100 A_(0))/(A._(0))`
`=130 kW//m^(2)`