A thin glass plate is placed in between a convex mirror of focal length 20cm and a point source. The distance between the glass plate and the mirror is 5cm. The image formed by the reflected rays from the front face of the glass plate and that due to the reflected rays by the convex mirror coincide at the same point. What is the distance of the glass plate from the source? Draw the ray diagram.

Explanation

In Fig. 1.41 the ray diagram has been shown. The distance between the glass plate M and the point source p=xcm (says). Light rays staring from p form the image at Q by reflection at the convex mirror. By the question, the plane glass plate also forms the image of P at Q.

`therefore` Distance of the image from the glass plate =xcm
`therefore` Distance of the image from the convex mirror = (x-5) cm and distance of the object from the convex mirror =-(x+5) cm
`"We know", (1)/(v)+(1)/(u)=(1)/(f) or, (1)/(x-5)+(1)/(-(x+5))=+(1)/(20)`
`or, " " (+x+5-x+5)/((x-5)(x+5))=+(1)/(20) or, (10)/(x^(2)-25)=+(1)/(20)`
`or, " " x^(2)-25=200 or, x^(2)=225 or, x=15cm`
`therefore` The distance of the glass plate from the source = 15cm.