Question

In the geometrical optics experiment, a student used a convex lens with 6 cm focal length to produce a large image of an object. The object was placed at a distance of 14 cm from the lens. What is the magnification of the image? include the sign.

Answer 1

Solution

In a convex lens all the light rays that enter parallel to its axis cross each other at a common point (focus) on the other side. If a point light source is placed on the focal point, the rays emerging from the lens will be parallel to each other. The rays passing through the centre of the lens does not change its path and is not diverted (negligible refraction).

The problem can be solved by using the thin lens equations,

1/d_o + 1/d_i =1/f , where,

d_o - distance of object from centre of lens = 14 cm.

d_i - distance of image from centre of lens.

f - focal length - distance of focus from centre of lens = 6 cm.

Substituting,

1/14 + 1/d_i = 1/6

gives, d_i = 10.5 cm

The magnification 'm' is given by :

m = d_i / d_o

Therefore, m = - 10.5/14 = -0.75 ..........(Ans.)

The minus sign indicates that the image is inverted.

The problem can also be solved by ray tracing method which is limited to the accuracy with which you draw.The thin lens equation produces more precise results limited only by the accuracy of the information given.

Figure below can help to solve using ray tracing method.Rays form the head of the person only is shown in figure. Similarly rays from all parts of the body helps in the image formation.