Combination of Lens

An eye specialist prescribes spectacles having a combination of convex lens of focal length 40 cm in contact with a concave lens of focal length 25 cm. The power of this lens combination in diopters is

Two thin lenses are of same focal lengths $f$, but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be:

In the figure shown here, what is the equivalent focal length of the combination of lenses (Assume that all layers are thin)?

Find equivalent focal length due to combination of two convex lens are in contact having a focal length both of them $30 \mathrm{cm}$.

A biconvex lens of radius of curvature $R$is made up of a variable refractive index $\mu =2\left(1+\frac{\left|y\right|}{d}\right)$. Assume $2 d<<R$. A point object is placed at $R=1 \mathrm{m}$ on the principal axis as shown in figure. If the spread of image lies over a span of $n$ meter along the axis, then find the value of $n$.

The radius of curvature of convex surface of a Plano-convex lens is $15 \mathrm{cm}$. The $\mathrm{R}.\mathrm{I}.$ of material of lens is $\frac{3}{2}$. When kept in air has focal length $f$. If plane surface is silvered and lens is kept in a large medium of $\mathrm{R}.\mathrm{I}.$ $=2$, it behave as a mirror of power $P$

Two thin lenses are put close to each other. The focal length of one of the lenses is $20 \mathrm{cm}$. If the focal length of the combination is $12 \mathrm{cm}$, then the focal length of the other lens is:

Two lenses of focal lengths 0.20 m and 0.30 m are kept in contact with each other. Calculate the resultant focal length of the combination. Also calculate the powers of the individual lenses and that of the equivalent lens.

The focal length of the combination of a convex lens of focal length $30 \mathrm{cm}$ in contact with a concave lens of focal length $20 \mathrm{cm}$. Is the system a converging or a diverging lens?

Two lenses with powers;$2\mathrm{D} \& -4\mathrm{D}$ are kept together. What is the effective focal length of the combination?

The effective focal length for lenses in contact is _____.

There is a convex lens of focal length $5 \mathrm{cm}$ and a concave lens of focal length $10 \mathrm{cm}$ are kept in contact. Calculate the equivalent focal length of the combination.

A concave lens of focal length $30 \mathrm{cm}$ placed in contact with a plane mirror acts as a:

The lenses of power $+ 3.5 \mathrm{D}$, $+ 2.5 \mathrm{D}$ and $+ 1 \mathrm{D}$ are placed in contact with each other in an optical device. The effective power of combination of these lenses is :

As shown in the figure, an equiconvex lens of refractive index $\mu =\frac{3}{2}$ is placed over a plane mirror. An object placed $12 \mathrm{cm}$ from the system such that image and object coincide. Now a liquid of refractive index ${\mu }_{\mathrm{L}}$ is poured between mirror and lens and for the same object the image now formed at $24 \mathrm{cm}$ from mirror. Find ${\mu }_{\mathrm{L}}$.

Derive an expression for the effective (equivalent) focal length of two thin lenses in contact.

The powers of two lenses in contact are $-15D$and $+5D$. What is the equivalent power?

A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of 10cm. The separation between the two lenses is 2cm. The focal lengths of the component lenses

Which of the following system of lens should be placed in the box P if the incident rays $I_1 and I_2$ has $I{\text{'}}_1 and I{\text{'}}_2$ as its refracted ray

Which of following system of lens should be placed in the box P if the incident rays$I_1$  and $I_2$ has$I{\text{'}}_1$  and$I{\text{'}}_2$  as its refracted ray.