Question

A dung beetle's image located parallel to the central axis of a spherical mirror is exactly at 15 cm. If the focal length of the spherical mirror is 25 cm.

a) calculate the distance of the beetle from the spherical mirror?

help

Answer 1

If it is concave mirror then ,v = -15 and f = -25

using the formula   

where u = the distance of the object(dung beetle here) from the pole of the concave mirror

v = the distance of object's image from the pole of concave mirror

f = focal length of the cancave mirror

putting all given values in the above formula and get

1/u + 1/(-15) = 1/(-25) so we get 1/u = -1/9.375 implies that u = -9.375 cm, minus sign shows that the object and image both are at left side of the mirror.

It it is covex mirror:

same formula can be used but sign can be changed and therefore distances.

here v = 15cm and f = 25 cm (both have taken positive because both of are on the right side of the mirror)

putting these values to the above formula

1/u + 1/15 = 1/25 , so we get 1/u = -1/37.5 which implies u = -37.5 cm negative sign shows that the object is on the left side of the mirror.