A small object is placed 50 cm to the left of a thin convex lens of focal length 30 cm. A convexspherical mirror of radius of curvature 100 cm is placed to the right of the lens at a distanceof 50 cm. The mirror is tilted such that the axis of the mirror is at an angle @ = 30° to theaxis of the lens, as shown in the figure.f = 30 cm(-50,0)|0,0)R = 100 cm50 cm(50+50 75.-50) NaIf 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​

The object distance for the lens of focal length f = 30 cm is u = −50 cm. Apply lens formula, 1/v −1/u =1/f , to get the image distance v = 75 cm. Thus, image I1 by the lens is formed 25 cm behind the mirror. x O 50 cm 50 cm 25 cm I2 I1 Let us consider the case when mirror is not tilted. The image I1 will act as a virtual object with u = 25 cm for a convex mirror of focal length fm = R/2 = 50 cm. Apply the mirror formula, 1/v +1/u =1/f m , to get the image distance v = −50 cm. Thus, image I2 by the mirror is formed 50 cm left of the mirror (see figure) What happens to the image if mirror is tilted by an angle θ? Consider a ray along the principal axis of the lens. If mirror is not tilted then this ray starts from the object, refracts through the lens without deviation, incident normally on the mirror and finally comes to the image I2 after reflection from the mirror. If the mirror is tilted by an angle θ then this ray is incident on the mirror at an angle of incidence θ and reflected by the mirror with an angle of reflection θ and finally forms a new image at I 0 2 (see figure). Thus, the axis on which image lies makes an angle 2θ = 60◦ with the principal axis of the lens. Also, the image distance will remain same upto the first order of approximation (image distance will remain exactly same in case of plane mirror). Thus, (x, y) coordinates of the image are x = 50 − 50 cos 60◦ = 25 cm, y = 50 sin 60◦ = 25√ 3 cm.