Question

4.) You position a lens 120 cm from a lamp and use it to project an image of the lamp onto a screen. You measure that the image of the light is one-fourth as tall as the actual lamp. a.) Is the lens a converging lens or a diverging lens? b.) Is the image of the lamp upside right or upside down? c.) What is the focal length of the lens?

Answer 1

Solution:

Object distance (u)=120 cm

Magnification (m)= 1/4

a) The lens is a converging lens because only in converging lens real image is produced so that we can project it into the screen.

b) The image of the lamp is upside down because when a converging lens produced real image, it is inverted.

c) Focal length of the lens is 24 cm

Reason:

since image is inverted, magnification (m)= -1/4

Object distance (u)= -120 cm

From formula for magnification of lens

m= v/u

Or, -1/4= v/(-120)

Or, v= 120/4= 30 cm

Again lens formula,

(1/v) -(1/u) = 1/f

Or, (1/30)-(1/-120)=1/f

Or, 4-(-1)/120= 1/f

Or, 5/120 = 1/f

Or, f = 120/5= 24 cm