question_answer

A spherical concave mirror of focal length 10 cm is cut in two equal halves and is separated by a distance 4 mm as shown. A small object is kept at 30 cm from the mirrors and between the two halves as shown.

The distance between the images by halves of mirror will be

A) 4 mm

B) 6 mm

C) 9 mm

D) 12 mm

Correct Answer: B

Solution :

[b] 

\[\frac{1}{\upsilon }=\frac{1}{u}=\frac{1}{f}\Rightarrow \,\frac{1}{\upsilon }+\frac{1}{-30}=\frac{1}{-10}\]\[\Rightarrow \,\,\frac{1}{\upsilon }=\frac{1}{30}-\frac{1}{10}=\frac{-2}{30}\]

\[\Rightarrow \]   \[\upsilon =-15\,cm\]

\[\therefore \]      \[m=-\frac{\upsilon }{u}=-\frac{-15}{-30}=-\frac{1}{2}\]

\[\therefore \]      Image-image distance \[=0.5+1+3+1.5\]\[=4+2=6\,\,mm\]