A slanted object AB is placed on one side of convex lens as shown in the diagram. The image is formed on the opposite side. Angle made by the image with principal axis is: [2025]

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Solution

Q.
A slanted object AB is placed on one side of convex lens as shown in the diagram. The image is formed on the opposite side. Angle made by the image with principal axis is: [2025]

1 $- \frac{α}{2}$

2 –45°

3 +45°

4 $- α$

Ans.
(2)

Location of image of A :

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{1}{v} - \frac{1}{- 30} = \frac{1}{20} \Rightarrow \frac{1}{v} = \frac{1}{60} \Rightarrow v = 60 cm$

$m = \frac{v}{u} = \frac{60}{- 30} = - 2$

Since size of object is small w.r.t. the location hence

$d v = m^{2} d u \Rightarrow d v = 4 \times 1 = 4 cm$

$d y = h_{i} = m h_{0} \Rightarrow h_{i} = 2 \times 2 = 4 cm$

$∴$ Angle made with principle axis = –45°

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