A 4.00-cm tall light bulb is placed a distance of 40 cm from a concave mirror having a focal length of 18 cm. Determine the image distance and the image size. (Hint: first determine the d_i and then use it to determine the h_i.)

 

Answer:

The image distance di = 32.73 cm

?(hi)Image Height = 3.28 cm

Step-by-step explanation

Given the following data

Object Height = 4.00-cm

Object distance = 40 cm

Focal length = 18 cm.

Determine the image distance and the image size. (Hint: first determine the diand then use it to determine thehi.)

Formula

1/do + 1/di = 1/f

Where do is the object distance = 40 cm

di is the image distance

f is the focal length = 18 cm

1/40 cm + 1/di = 1/18 cm

1/di = 1/18 cm - 1/40 cm

di = 32.73 cm

The image distance di = 32.73 cm

Magnification = Image distance/Object distance

Magnification = 32.73 cm/40 cm

Magnification = 0.81

Again Magnification = (hi)Image Height /(ho)Object Height

(hi)Image Height = Magnification x (ho)Object Height

Where (hi)Image Height = 4.00-cm

(hi)Image Height = 0.82 x 4.00-cm

(hi)Image Height = 3.28 cm