A student has obtained an image of a well-illuminated distant object on a screen to determine the focal length, F1of the given spherical mirror. The teacher then gave him another mirror of focal length, F2 and asked him to obtain a focused image of the same object on the same screen. The student found that in order to focus the same object using the second mirror, he has to move the mirror away from the screen. From this observation, it may be concluded that both the spherical mirrors given to the student were (select the correct option)

(A) Concave and F_{1} < F_{2}

(B) Concave and F_{1} > F_{2}

(C) Convex and F_{1} < F_{2}

(D) Convex and F_{1} > F_{2 }

#### Solution 1

(A) Concave and F_{1} < F_{2}

Since the image is focused, the spherical mirror is a concave mirror. For second mirror the distance is increased to focus the image on the screen. Hence, focal length is more than that of first mirror.

#### Solution 2

Real and inverted image is formed by the concave mirror. As mentioned, in the second case, the image distance (*v*) is increasing. Well-illuminated distant object i.e. object is at infinity.

Mirror formula is given by:-

`1/F=1/v+1/u`

`F=(vu)/(v+u)`

`=(uv)/(u(1+v/u))`

`"as u tends to infinity "v/u" is negleigible."`

Hence, F is directly proportional to v.

Therefore, F_{â1 }< F_{2}

Hence, the correct option is A.