A small object is placed 50 cm to the left of a thin convex lens of focal length 30 cm. A convex spherical mirror of radius of curvature 100 cm is placed to the right of the lens at a distance of 50 cm. The mirror is tilted such that the axis of the mirro

Question

A small object is placed 50 cm to the left of a thin convex lens of focal length 30 cm. A convex spherical mirror of radius of curvature 100 cm is placed to the right of the lens at a distance of 50 cm. The mirror is tilted such that the axis of the mirror is at an angle $θ = 30 °$ to the axis of the lens, as shown in the figure.

If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates (in cm) of the point $(x, y)$ at which the image is formed are [2016]

Smart Achievers · Accepted Answer

(3)

For convex lens, $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

$\Rightarrow \frac{1}{v} - \frac{1}{- 50} = \frac{1}{30}$ $(∵ v = - 50 cm, f = 30 cm)$

$∴$ $v = 75 cm$

The image formed by the convex lens acts as an object for the mirror.

For mirror, $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ $∴$ $\frac{1}{v} + \frac{1}{25} = \frac{1}{50}$ $∴$ $v = - 50 cm$

The image $I$ would have formed as shown had the mirror been straight. But here the mirror is tilted by $30 °$ . Therefore, the image will be tilted by $60 °$ and will be formed at A.

Here, $M A = 50 \cos 60 ° = 25 cm$ ( $x$ -coordinate of the image) and $I' A = 50 \sin 60 ° = 25 \sqrt{3} cm$ ( $y$ -coordinate of the image)

Hence, the coordinates of the point at which the image is formed are $(25, 25 \sqrt{3})$

Solution

1 $(0, 0)$

2 $(50 - 25 \sqrt{3}, 25)$

3 $(25, 25 \sqrt{3})$

4 $(125 / 3, 25 \sqrt{3})$

Want Us to Email you About Special Offers & Updates?

Solution

1 (0, 0)

2 (50−253, 25)

3 (25, 253)

4 (125/3, 253)

Want Us to Email you About Special Offers & Updates?

1 $(0, 0)$

2 $(50 - 25 \sqrt{3}, 25)$

3 $(25, 25 \sqrt{3})$

4 $(125 / 3, 25 \sqrt{3})$