converging mirror

Question

A 5.0 cm high object is placed 2.5 cm in front of a converging mirror and the image is magnified -3.0 x.

The distance to the image is: ___ cm

The focal length of the mirror is ___ cm

Answer 1

1)

Convrging mirror means Concave mirror.

Object height h_object  = 5 cm

Distance of the object d_object = 2.5 cm

The magnification M = -3x

M = - (d_image)/(d_object)

-3 = - (d_image)/(2.5) ⇒ 3 = (d_image)/(2.5)

d_image = 3(2.5) = 7.5 cm

Distance to the image is 7.5 cm.

Answer 2

2)

f = Focal Length.

Formula : (1/f) = (1/d_object) + (1/d_image)

(1/f) = (1/2.5) + (1/7.5)

(1/f) = (10/25) + (10/75)

Rewrite the expression with common denominator.( LCM of 25 and 75 is 75 )

(1/f) = (10*3-10*1)/75

(1/f) = (30-10)/75 ⇒ (1/f) = 20/75 ⇒ (1/f) = (1/3.75)

f = 3.75 cm

Focal Length is 3.75 cm.