Question

When an object is placed at a distance of 50 cm from a concave spherical mirror, the magnfication produced is -1/2 where should the object be placed to get a magnification of -1/5?​

Answer 1

ANSWER:

200cm

${\huge{\boxed{\mathcal{\red{Explanation}}}}}$

An object is said to be magnified when size of its image is more than its size.

Magnification of an object is represent by v /u

Where :

• v = Image distance
• u = Object distance

Now according to Magnification formula :

Magnification is equals to :

$\frac{f}{f - u}$

Where :

• f = focal length
• u = object distance

Now In the first case, it is given :-

• Image distance = -50cm. (-) due to sign convention
• Magnification = -1/5

So after inputting these values in magnification formula we get :

$\frac{ - 1}{2} = \frac{ f}{( f) - 50}$

$\frac{f + 50}{2} = f$

$f + 50 = 2f \\ 50 = 2f - f \\ f = 50cm$

Now we get focal length of given mirror is 50cm, which, is a constant value.

Thys applying this magnification in the second case we get :

$\frac{ - 1}{5} = \frac{50}{50 - u}$

$50 + u = 50 \times 5$

$50 + u = 250 \\ u = 250 - 50 \\ u = 200cm$

Thus the object should be placed at 200cm to get a magnification of -1/5.

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BY SCIVIBHANSHU

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