Question

1. An object 2 cm high is placed in front of a concave lens of focal length 3 cm, at a distance of 5 cm from the optical centre of lens. Draw a neat ray diagram using above dimensions and locate the position of image.
2. From the diagram state four characteristics of image.

Answer 1

(a) Ray Diagram and Image Location:

To find the exact position mathematically before drawing, we use the lens formula:

\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]

Given values according to Cartesian sign convention:

Height of object (h₁) = +2 cm

Focal length of concave lens (f) = −3 cm

Object distance (u) = −5 cm

Calculation:

\[ \frac{1}{-3} = \frac{1}{v} - \frac{1}{-5} \]

\[ -\frac{1}{3} = \frac{1}{v} + \frac{1}{5} \]

\[ \frac{1}{v} = -\frac{1}{3} - \frac{1}{5} \]

\[ \frac{1}{v} = \frac{-5 - 3}{15}\]

\[ \frac{1}{v} = -\frac{8}{15} \]

\[ v = -\frac{15}{8}\]

v = −1.875 cm

The image is formed at a distance of 1.875 cm in front of the lens (on the same side as the object).

(b) Based on the ray diagram and calculations, the four characteristics of the image are:

1. Virtual: It is formed by the actual divergence of light rays, meaning it cannot be caught on a screen.
2. Erect: The image points upwards in the same vertical orientation as the original object.
3. Diminished: The height of the image is visibly smaller than the object height.
4. Positioned between Focus and Optical Centre: It is located on the same side as the object, specifically at a distance of 1.875 cm from the lens.