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?

a) The mirror is concave

b) The focal length of the mirror = -1.25m or -5/4 m

Step-by-step explanation:

a) Determine whether the mirror is convex or concave?

A concave mirror is a spherical mirror that it's magnification is equal to, less than or more than 1 while a convex mirror is a mirror whereby it magnification is always less than one.

From the above question we are told that the spherical mirror is magnified 5 times.

Hence, because the spherical mirror is magnified 5, it is a concave mirror.

b) Magnification = - image distance/ object distance

Magnification = 5

Image distance = 5m

Object distance = ???

5 = -5/Object distance

Object distance = -5/5

= -1m

Formula for focal length =

1/f = 1/v + 1/u

v = image distance = 5

u = object distance = -1

1/f = 1/5 +1/-1

1/f = 1/5 - 1

1/f = -4/5

f = -5/4

f = -1.25m

The focal length of the mirror = -1.25m

angles 1 and 3 are vertical angles, meaning that they are equal to each other. to solve this you may set angle 1 and 3 equal to each other and just solve for x like

110 = 2x + 10

100 = 2x

50 = x

check:

110 = 2* 50 + 10

110 = 100 + 10

110 = 110

hope this !

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