Question

Q3 '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 @ = 30° to the
axis of the lens, as shown in the figure.
f = 30 cm
(-50,0)
|0,0)
R = 100 cm
50 cm
(50+50 75.-50) Na
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​

Answer 1

The image is formed at the coordinates (25, 25 √3 cm)

Explanation:

For lens 1 / v − 1 / u = 1 / f

1 / v − 1 / − 50 = 1 / 30

V = 75 cm

Therefore object distance for mirror is 25 cm and object is virtual.

For minor 1 / v + 1 / u = 1 / f

1 / v + 1 / v + 1 / 25 = 1 / 50

v = − 50 cm

Here the mirror is tilted by 30 degree. Therefore the image will be tilted by 60 degree and will be formed at A.

Here MA = 50 cos 60 degree = 25 cm

IA = 50 sin (60°) = 25 √3 cm

Thus the image is formed at the coordinates (25, 25 √3 cm)