Numerical Problems on Mirror

An object is kept in front of a concave mirror of focal length 20 cm. The image formed is 3 times the size of object. Calculate the possible distance of object from the mirror.

As the size of image is three times of size of object then magnification m = 3

If the image formed here is real then, -3 = –  or, v = 3u

Object distance u = -x

Image distance v = -3x

Focal length f = – 20 cm

Using the mirror formula we get,

Or,

Or,

 x =  = 26.6 cm.

If the image is formed here is virtual then, 3 = –  or, v = – 3u

Object distance u = -x

Image distance v = 3x

Focal length f = – 20 cm

Using the mirror formula we get,

Or,

Or,

 x =  = 13.3 cm.

The possible distance of object from the pole of the mirror are respectively – 26.6 cm and -13.3 cm.

The sun (diameter d) substances an angle radian at the pole of a concave mirror of focal length f. Calculate the diameter of the image of the sun formed by the mirror.

As the sun is at a far distance from earth then object distance u = . Therefore, the image of the sun is at the focus of mirror. So, v = f. The angle subtended by the incident and reflected ray at the pole of the mirror is very small. Therefore, tan = .

If the diameter of the image of the sun is A/B/ then from the diagram,

Or,

  .

Use of concave mirror:

1. Concave mirror are used by dentist, as shaving mirror or in make up because when the teeth or face is kept between the pole and focus of the mirror, it gives virtual erect and magnified image.

2. Large concave mirror are used to concentrate sunlight in solar heating device. The substance to be heated is placed at the focus of the concave mirror, where the sunlight converges after reflection.

3. Concave mirrors are used in reflecting telescope.

4. Concave, paraboloid mirrors are used in search light, motor head light. If the bulb is placed at focus of the mirror then light travels a large distance.

 Use of convex mirror:

1. convex mirror is used as a rear view mirror because it produce erect and diminished image. Since the image in small in size, so the field of view behind the vehicle is increased.

2. It is used in big shops to monitor the customers.

Paraxial rays, marginal rays:

Paraxial rays: Those rays which incident on the spherical mirror near to the principle axis of the mirror are called paraxial ray.

Marginal Ray: Those rays incident on the mirror just closer to the edge of the mirror is called marginal ray.