The focal length of a concave mirror is 30 cm. An object is placed at a distance of 45 cm in front of the mirror. A plane mirror is placed perpendicularly on the principal axis of the concave mirror in such a way that the object is situated in between the two mirrors. Light rays from the object at first are reflection from the concave mirror and then from the plane mirror. As a result the final image coincides with the object. What is the distance between the two mirros?

Explanation

In case of the concave mirror `M_(1)M_(2),` P is the object and P' is its image [Fig.1.45].
`Here, " " u=-45 cm, f=-30cm`
`"We know", (1)/(v)+(1)/(u)=(1)/(F) or, (1)/(v)-(1)/(45)=-(1)/(30)`
`or, " " (1)/(v)=-(1)/(30)+(1)/(45)=(-3+2)/(90)=-(1)/(90) or, v=-90 cm`
`therefore " " OP' = 90 cm`

According to the question, the reflected rays from the concave mirror form the final image at P afte reflection from the plane mirror M .
`therefore " " PM = P'M = x (say)`
`"Here", " " OP' = OP + PM + P'M`
`or, " " 90=45+x+x or, x=(45)/(2)=22.5 cm`
`therefore` Distance between the