Question

Examining your image in a convex mirror whose radius of curvature is 25.8 cm , you stand with the tip of your nose 11.0 cm from the surface of the mirror.

Where is the image of your nose located?

What is its magnification?

Your ear is 10.0 cm behind the tip of your nose; where is the image of your ear located?

What is its magnification?

thank you!!

Answer 1

Part 1.

Radius of curvature of mirror,R=25.8 cm

So

Focal length of mirror,f=R/2=25.8 cm/2=12.9 cm

Distance of tip of nose from mirror is,d_o=11 cm

Let the distance of image is =d_i

According to mirror equation

1/f=1/d_o+1/d_i

so

d_i=(fd_o)/(d_o-f)=(12.911)/(11-12.9)=-74.68 cm

distance of image of tip of nose is=-74.68 cm

Magnification=d_i/d_o=74.68/11=-6.79

Part 2.

Distance of ear from mirror is,d_o=11 cm+10 cm=21 cm

d_i=(fd_o)/(d_o-f)=(12.921)/(21-12.9)=33.44 cm

distance of image of ear=33.44 cm

magnification=d_i/d_o=33.44/21=1.6