Problem on Focal length

Topic:-Focal length

The focal length of an optical system is a measure of how strongly it converges (focuses) or diverges (defocuses) light. A system with a shorter focal length has greater optical power than one with a long focal length; that is, it bends the pencil of rays more strongly, bringing them to a focus in a shorter distance.

Question :-

A girl is applying make-up in a concave mirror. Her face is 35cm in front of the mirror. The image is 72cm behind the mirror. Using the mirror equation find the focal length of the mirror. What is the magnification of the image?

ANSWER:

Focal length of the mirror=68.108 cm, Magnification of the image=2.057

The mirror equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f). The equation is stated as follows:


1/f=1/ do +1/ di

do=35 cm

di=-72 cm

1/f=1/35-1/72

Focal length = f=68.108 cm

The magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (hi) and object height (ho).

m = - di/ do=-(-72)/35= 2.057

The magnification of the image=2.057.