Question

The focal length of concave mirror is f and the distance of the object from the principle focus is a.the magnitude of magnification obtained will be:-
1.)(f+a)f
2.)f/f-a
3.)f/(f+a)
4.)f^2/a^2

Answer 1

Given that, the focal length of the concave mirror is f and the distance of the object from the principle focus is a.

Object distance (u) from the concave mirror is (f + a)

Now, the object always placed on the left side of the mirror. So, object distance = -(f + a) = (-f - a)

Mirror formula:

1/f = 1/v + 1/u

(In concave mirror focal length is negative)

Substitute the value of 'u' above

1/(-f) = 1/v + 1/(-f - a)

-1/f - 1/(-f - a) = 1/v

-1/f - (-1)/(f + a) = 1/v

-1/f + 1/(f + a) = 1/v

(-f - a + f)/[f(f + a)] = 1/v

(-a)/(f² + fa) = 1/v

v = [(-f)(f + a)]/a

Now,

m = -v/u

m = -[(-f)(f + a)/a] / [-(f + a)]

m = [(-f)(f + a)/a] / (f + a)

m = [(-f)(f + a)]/[a(f + a)]

m = -f/a

(None of the given option)

Answer 2

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QUESTION :

The focal length of concave mirror is f and the distance of the object from the principle focus is a.the magnitude of magnification obtained will be:-

1.)(f+a)f

2.)f/f-a

3.)f/(f+a)

4.)f^2/a^2

SOLUTION :

Object Distance = -f - a.

Using the mirror Formula,

1/u + 1/v = 1/f

Hence :

1/(-f) = 1/v + 1/(-f - a)

-1/f - 1/(-f - a) = 1/v

-1/f - (-1)/(f + a) = 1/v

-1/f + 1/(f + a) = 1/v

(-f - a + f)/[f(f + a)] = 1/v

(-a)/(f² + fa) = 1/v

v = [(-f)(f + a)]/a

Magnification = - v / u.

=> m = -[(-f)(f + a)/a] / [-(f + a)]

m = [(-f)(f + a)/a] / (f + a)

m = [(-f)(f + a)]/[a(f + a)]

m = -f/a........(A)