question_answer

A concave mirror of focal length \[100cm\] is used to obtain the image of the sun which subtends an angle of \[30{}^\circ .\] The diameter of the image of the sun will be

A)            \[1.74cm\]                            

B)            \[0.87cm\]

C)            \[0.435cm\]                          

D)            \[100cm\]

Correct Answer: B

Solution :

                   The angle subtended by the image of the sun at the mirror \[=3{0}'={{\left( \frac{1}{2} \right)}^{o}}=\frac{\pi }{360}\,\,rad\]                    If \[x\] be the diameter of the image of the sun, then            \[\frac{\text{Arc}}{\text{Radius}}=\frac{x}{100}=\frac{1}{2}.\frac{2\pi }{360}=\frac{\pi }{360}\]\[\Rightarrow \,\,x=\frac{100\pi }{360}=0.87\,cm\]