The diameter of the sun subtends an angle of `0.5^(@)` at the pole of the concave mirror. The radius of curvature of the mirror is 1.5 m. Find the diameter of the image of the sun. Consider the distance of sun from the mirror infinite

Explanation

Image of the sun due to given concave mirror is shown in the figure
Suppose diameter of sun is `D_s` and diameter of its image is `D_i`
From the figure `D_i= 2BF`
As the sun rays coming from the far distance its image is formed on the focal point F ofconcave mirror.

`therefore` Image distance v = PF = f (focal length ) and if diameter of sun formed angle `alpha` at the pole of mirror,
In `Delta PFB, angle PFB = (alpha)/92 = (0.5^@)/(2) = ` will be `0.25^@` and ` tan (alpha)/(2) = (BF)/(PF)`
`= (D_i)/(2f) [ because @BF = D_i and PF = f]`
`therefore D_ = 2f xx tan (alpha)/(2)`
`= 2 xx 75 xx tan(0.25^@)`
`= 150 xx 0.00435 = 0.6525 cm `