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?
None of the choices is correct.
Ans: The focal length of the mirror will be 10 cm.
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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