Question

aur 2.5 CM candle is placed 12 CM away from a convex mirror of focal length 30 cm give the location of the image and the magnification. give whole explaination​

Answer 1

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Image distance = 20cm

Magnification = -5/3

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It is given that :-

Height of object = 2.5cm

Object distance = 12cm from pole of mirror = -12( due to sign convention)

Focal length of mirror = 30cm

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Now according to mirror formula :

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

$f = \frac{uv}{u + v}$

After inputting the known values we get :

$30 = \frac{ - 12v}{12 - v} \\ \\ 360 - 30v = - 12v \\ 360 = - 12v + 30v \\ 360 = 18v \\ v = \frac{360}{18} \\ v = 20cm$

Now we got that the image forms at a distance of 20cm from pole of mirror.

Now we know, that for an object magnification of its image is the ratio of its image distance to object distance, mathematically it is represented by :

$m = \frac{ - v}{u}$

After inputting the values we get :

$m = \frac{ - 20}{12} = \frac{ - 5}{3} cm$

Thus magnification of image is -5/3 cm.

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BY SCIVIBHANSHU

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