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An image of a linear object due to a con...

An image of a linear object due to a convex mirror is `1/4 th` of the length of the object .
If focal length of the mirror is 10 cm , find the distance between the object and the image. The linear object is kept perpedicular to the axis of the mirror.

Text Solution

Verified by Experts

Mgnification of image `m = - (v)/(u) = (h.)/(h) = 1/4`
`therefore v = - u/4`
Here, f = 10 cm ,`m = 1/4` v = ? , u +v = ?
Using Gauss law
`1/f = 1/u + 1/v`
`therefore 1/10 = 1/u -(4)/u`
`therefore 1/10 = - (3)/u`
`therefore u = - 30 cm `
Again using Gauss law ,
`(1)/(v) = 1/f - (1)/(u) = (1)/(10) + (1)/(30)`
`therefore v = 30/4 = 7.5 cm`
`therefore ` Distance between object and image
` h = u + v = | - 30 | + 7.5`
`therefore u + v = 37.5 cm `
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