EXERCISE 14

An object is placed at a distance of $8 \mathrm{cm}$ on the axis of and one side of a convex lens of focal length $16 \mathrm{cm}$. A second convex lens of focal length $10 \mathrm{cm}$ is placed co-axially on the other side of it and at a distance of $5 \mathrm{cm}$ from the first lens. Find the position and magnification of the final image formed by the lens combination.

A pin is placed $10 \mathrm{cm}$ in front of a convex lens of focal length $20 \mathrm{cm}$ made of a material of r . i .$1.5$ . The surface of the lens further away from the pin is silvered and has a radius of curvature $22 \mathrm{cm}$. Determine the position of the final image. Is the image real or virtual ?

A convex lens of focal length $f$ produced an image of an object $m$ times magnified on a screen. If $x$ be the distance between the object and the screen, show that $\mathrm{f}=\frac{\mathrm{xm}}{(1+\mathrm{m}{)}^2}$.

When an object is placed $60 \mathrm{cm}$ away from a lens, its image is formed on the other side of the lens at a distance of $300 \mathrm{cm}$ from the lens. If the object is moved by $20 \mathrm{cm}$ towards the lens, find the new position of the image.

An equiconvex lens of r.i. $1.5$ and focal length $10 \mathrm{cm}$ is so placed that the upper half of the lens is in air and lower half immersed in water of r.i. $4/3$. An object is placed in air along the vertical axis at a distance of $50 \mathrm{cm}$ from the lens. At what distance from the lens will the image be focussed?

A concave lens is placed at a distance of $25 \mathrm{cm}$ in front of a concave mirror of focal length $20 \mathrm{cm}$. It is found that a pin placed at a distance of $68.6 \mathrm{cm}$ in front of the lens coincides with its own inverted image formed by the lens and the mirror. Find the focal length of the lens.

The radii of curvature of both the surface of a concave lens made of glass $(\mathrm{\mu }=1.5)$ are each equal to $R$. Show that the lens will behave as a convex lens of focal length $3.5\mathrm{R}$ when immersed in a medium of r.i. $1.75$

A particle executes S.H.M. of amplitude $1 \mathrm{cm}$ along the principal axis of a convex lens of focal length $12 \mathrm{cm}$. The mean position of the oscillation is $20 \mathrm{cm}$ from the lens. Find the amplitude of oscillation of the image of the particle.