Three times magnified image of an object is formed on a screen placed at a distance of 8 cm from the object with the help of the spherical mirror. Determine the nature of the mirror. Focal length and the distance the mirror from the object.

Explanation

Since the image of formed on a screen, so the image real the mirror is concave [Fig.1.49].
Suppose, `u= x cm and so v = (x+8) cm`
Here, `m = 3 or, (v)/(u)=3` [taking the mod value of m]
`or, " " (v)/(u)=3 or, ((x+8))/(x)=3 or, x=4 cm`
So, the mirror is situated at a distance of 4 cm from the object
`therefore " " v=(4+8) = 12 cm `
`"We know", (1)/(v)+(1)/(u) = (1)/(f)`
`or, " " (1)/(-12) +(1)/(-4)=(1)/(f)`
`or, " " f = -3 cm`

`therefore` Focal lenght of the mirror
= 3 cm. Negative sign in the value of f supports the mirror cancave in nature.