Question

# An object is placed 10-cm from a convex mirror. An image 0.5 times the size of...

An object is placed 10-cm from a convex mirror. An image 0.5 times the size of the object is formed. What is the focal length of the mirror?

 –10 cm +10 cm None of the choices is correct. +5 cm –5 cm

Ans: The focal length of the mirror will be 10 cm.

Explanation:

Here we are given a convex mirror,

Object distance (given)=u= -10cm (by considering the sign convention)

Let, the image distance be= v

We will apply the mirror equation to find focal length, that is Now, here we don't have the value of 'v'.

So, using magnification formula of mirror, that is

m = -v/u also, m= hi/ho (where, hi= image size and ho=object size)

Comparing both formulas, we get

-v/u = hi/ho

Substituting the given values, u=-10 cm and hi=0.5ho , we get

-v/(-10) = 0.5 ho/ho

Solving further, we get

v= 5 cm

Now substituting the value of 'v' and 'u' in the mirror formula:

1/f =1/v + 1/u

1/f= 1/5 + 1/(-10) (because 'u' is always taken negative)

1/f = 1/5 - 1/10

1/f = (10-5)/(5x10)

1/f = 1/10

f = 10 cm

Hence , the focal length of the given convex mirror is 10 cm.

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