Question

You are looking toward a concave spherical mirror whose radius of curvature is 20 cm. Your line of sight is parallel to (but not along) the principal axis. How far from the mirror does your line of sight cross the principal axis?

Answer 1

We use the mirror formula to find the distance at which the line of sight cross the principal axis.

The mirror formula is

1/u + 1/v = 1/f     ........(1)

u is the object distance, v is the image distance, f is the focal length of the mirror.

We will follow the sign convention that the distance measured to the left of mirror are negative and the distance measured to the right of mirror are positive.

In our case since we are looking parallel to the concave mirror our line of sight is at infinity. So u = - ,

also we know that for a spherical mirror f = R/2

R is the radius of curvature of lens. Given R = 20 cm

f = 20/2

f = -10 cm (since the focal legth is to the left of the mirror in case of concave lens

We need to find the value of v. Putting all the values in eq. (1) we get

1/- + 1/v = 1/(-10)

0 + 1/v = -1/10

1/v = -1/10

v = -10 cm

Therefore the line of sight crossed the principal axis at a distance of 10 cm. The negative sign indicates that the distance is to the left of the mirror.