Question

at what distance from a convex mirror having focal length 5 m should an object be placed so that the image has a height equal to 1/3 of the original height also find the distance between object and image​

Answer 1

Object distance = 3(5m)  = 15 m

Explanation:

From the formula, we have

Magnification = height of the image/height of the object=-image distance/object distance

Given

Height of object = x

Height of image = x/3

Image distance = v

Object distance = u

Putting in the formula, we get

$\frac{\frac{x}{3} }{x}=-\frac{v}{u}$

$\frac{x}{3} *\frac{1}{x} =-\frac{v}{u}$

$\frac{1}{3} =-\frac{v}{u}$

If we use sign conversion

u = 3v

This shows that the object will be placed at a distance three times the distance of the image.

Now, by putting the value of the focal length, we can find out the exact distance

Object distance = 3(5m)  = 15 m

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