A spherical mirror gives an image magnified 5 times at a distance 5 m. determine whether the mirror is convex or concave? How much will be the focal length of the mirror?

1. Concave mirror.

2. 4.17 m or 417 cm.

Explanation:

The following data were obtained from the question:

Object distance (u) = 5 m

Magnification (M) = 5

Focal length (f) =..?

1. Identification of the mirror.

To determine whether or not the mirror is concave or convex, we must first of all calculate the image distance.

This can be obtained as follow:

Object distance (u) = 5 m

Magnification (M) = 5

Image distance (v) =.?

Magnification (M) = image distance (v) /object distance (u).

M = v/u

5 = v/5

Cross multiply

v = 5 x 5

v = 25 m

Since the image distance obtained is positive, the mirror is said to be a concave mirror.

2. Determination of the focal length of the mirro.

This can be obtained as follow:

Object distance (u) = 5 m

Image distance (v) = 25 m

Focal length (f) =...?

1/f = 1/v + 1/u

1/f = 1/25 + 1/5

1/f = 0.04 + 0.2

1/f = 0.24

Cross multiply

f x 0.24 = 1

Divide both side by 0.24

f = 1/0.24

f = 4.17 m

Converting the focal length of cm, we have:

1 m = 100 cm

Therefore, 4.17 m = 4.17 x 100 = 417 cm

Therefore, the focal length of the mirror is 4.17 or 417 cm.

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