The sun subtends an angle `theta` radians at the pole of a concave mirror of focal length f. What is the diameter of the image of the sun formed by the mirror.

Options

A. ` 2 f theta `
B. ` ( f theta ) /( 2 ) `
C. ` f theta `
D. ` ( f ) /( theta ) `

Answer

C

Explanation

Since the sun is at large distance very distant , u is very large and so ` (1 ) / ( u ) ~~ 0 `
`rArr therefore ( 1 ) /( v ) + ( 1 ) /( u ) = ( 1 ) /( f ) rArr ( 1 ) /( v ) = - ( 1 ) / (f ) rArr v = - f `

The image of sun will be formed at the focus and will be real, inverted and diminished A'B' = height of image and
` theta = (Arc ) /("Radius") = ( A'B ) /( FP ) rArr theta = ( d ) / ( f ) rArr d =f theta `