To find the focal length of concave mirror by using u-v method

Spherical mirrors are a piece of hollow glass sphere being cut by a plane. One surface of the spherical mirror is polished and the other is reflecting. Spherical Mirrors are of two type:

Concave mirrors and convex mirrors. The mirror in which the outer bulge surface is polished and the reflection of light takes place from the inner hollow surface is known as concave mirror whereas the mirror whose inner surface is polished and reflection of light takes place from the outer surface is known as convex mirror.

Concave mirrors

The mirror in which reflection takes place from the hollow inner surface and has polished outer surface. It is used in headlights, solar furnaces, shaving mirrors, head mirrors etc.

Terms associated with the spherical Mirrors

Pole(P):  it is the centre of the spherical mirror.

Centre of curvature(C):  it is the centre of sphere of which the mirror forms a part.

Principal axis: the line passing through the pole and the centre of curvature of the mirror is known as principal axis.

Linear aperture:  it is the diameter of the circular boundary of the spherical mirror.

Angular aperture: it is the angle subtended by the boundary of the spherical mirror at its centre of curvature.

Principal focus: a beam of light parallel to the principal axis either converges to or appears to diverge from a point F on the principal Axis after reflection from the spherical mirror. This point F is known as the principal focus of the mirror.

Focal length: the distance between the focus and the pole of the mirror is a focal length of the mirror.

Focal plane:  the vertical plane passing through the principal focus and perpendicular to the principal axis is called focal plane.

• Relationship between focal length and radius of curvature:

               focal length= 1/2* radius of curvature

Mirror formula:

1/f = 1/v + 1/u 

f = uv / (u+v).

f= focal length of concave mirror

u= distance of object from the mirror

v= distance of image from the mirror

How to find the focal length of the concave mirror by u-v method

Aim:   to find the focal length of a concave mirror by using u-v method.

Material used:  concave mirror, stand, screen, illuminated wire gauze, metre scale etc.

Procedure to find focal length:

First we have to find the focal length of a mirror by distance object method.

• Fix the concave mirror on the stand and now put the stand in front of the screen in such a way that the image of the object should be visible on screen.
• Adjust the mirror to get the clear image of an object.
• Measure the difference between mirror and the screen using a metre scale. The length between screen and mirror is the focal length (f ) of the mirror.
• Now by using the focal length obtained, say the value of you that is the distance between mirror and object ranging from 1.5f to 2.5f now, divide the range into a number of equal steps.
• Place the mirror in front of an illuminated wire gauze and it will act as an object.
• Now fix the mirror at the distance you have which is equal to 1.5 f from the wire gauze.
• Place the screen in front of a mirror in such a way that the reflection of the image lies on the screen.
• Now it’s just the position of the screen to get the clear image of the wire gauze.
• Measure the distance between mirror and wire gauze (u) and the distance between mirror and screen (v). 
• Record the values of u and v in a tabular format.
• Now calculate the focal length of a concave mirror by using the relation, f = uv / (u+v).
• Repeat the experiment to obtain different values of you and in each time measure we and record it in the table.
• Calculate the focal length of a mirror each time.
• Now calculate the mean of all the focal lengths to get the correct focal length of the given concave mirror.

Conclusion 

Spherical mirror are those whose reflecting surfaces form part of hollow sphere spherical. Mirrors are of two types: concave mirror & convex mirror. Concave mirror: in which the reflection of light takes place from the inner hollow surface. Convex mirror: in which the reflection of light takes place from the outer bulb surface. Important terms related to spherical mirror are: Pole, centre of curvature, radius of curvature, principal axis, linear aperture, angular aperture, principal focus, focal length, focal plane.