Question

An object AB is placed on the principal axis of a convex lens as shown in the diagram.

Copy the diagram according to dimensions.

1. From point A draw a ray passing through optical centre and then to the other side of lens.
2. From point A draw a ray parallel to principal axis and then its passage through convex lens after refraction.
3. From point A draw another ray passing through F₁ and then through lens after refraction.
4. Locate the position of image.
5. State two characteristics of image.

Answer 1

(a) The ray from A through the optical centre O goes straight through without bending.

(b) The ray from A parallel to the principal axis bends at the lens and passes through F₂.

(c) The ray from A through F₁ comes out of the lens parallel to the principal axis.

(d) The three rays meet at A′, below the axis, beyond 2F₂ on the other side of the lens. The image A′B′ is formed there, 7.5 cm from the lens and 1.5 cm high.

The lens formula confirms this:

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

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

\[ \Rightarrow \frac{1}{v} = \frac{1}{3} - \frac{1}{5} = \frac{2}{15} \]

\[ \Rightarrow v = + \ 7.5 \ \text{cm} \]

\[ m = \frac{v}{u} = \frac{7.5}{-5} = - \ 1.5 \]

(e) Two characteristics of the image:

1. Real and Inverted: The image is formed by the actual intersection of refracted light rays and points downwards below the principal axis.
2. Magnified: The size of the image is larger than the object (Height = 1.5 cm, compared to the 1 cm object height).