Question

The correct relation between magnification m, object distance u and focal length f of a spherical mirror is

Answer 1

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Answer 2

The correct relation between magnification m, object distance u, and focal length f of a spherical mirror is m = f/(f - u) .

We know that the magnification of a spherical mirror is given by the formula:

m = - v/u

where v is the image distance

and u is the object distance

This equation could be rewritten as v = -mu. Let this be equation 1

Now, we also know the mirror formula, to obtain the reciprocal of focal length f, which is 1/f = 1/v + 1/u. Let this be equation 2

Now, substitute equation 1 in equation 2. We get:

1/f = 1/(-mu) + 1/u

⇒ 1/f = -1/mu + m/mu

⇒ 1/f = (m-1)/mu

⇒ f = mu/(m-1)

⇒ f(m-1) = mu

⇒ fm - f = mu

⇒ fm - mu = f

⇒ m(f - u) = f

⇒ m = f/(f - u)

This is the correct relation between magnification m, object distance u, and focal length f of a spherical mirror

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