Refraction through Spherical Surface and Lens

An object is placed in front of a thin convex lens of focal length 30 cm and a plane mirror is placed 15 cm behind the lens. If the final image of the object coincides with the object, the distance of the object from the lens is

A thin lens of focal length $f$and its aperture has a diameter $d$. It forms an image of intensity $I$. Now the central part of the aperture upto diameter $\frac{d}{2}$ is blocked by an opaque paper. The focal length and image intensity would change to

Parallel beam of light is incident on a system of two convex lenses of focal lengths $f_1=20 \mathrm{cm}$ and $f_2=10 \mathrm{cm}$. What should be the distance between the two lenses so that rays after refraction from both the lenses pass undeviated

A plano-convex lens $\left(\mu =\text{1.5}\right)$ has maximum thickness of 1 mm. If diameter of its aperture is 4 cm, then, the radius of curvature of curved surface and its focal length in air are respectively 

An objective is kept at a distance of $16 \mathrm{cm}$ from a thin lens and the image formed is real. If the object is kept at a distance of $6 \mathrm{cm}$ from the same lens the image formed is virtual. If the size of the images formed are equal, then find the focal length of the lens?

A double convex lens has focal length of $25.0 \mathrm{cm}$ in air. The radius of one of the surfaces is double of the other. Find the radii of curvature, if the refractive index of the material of the lens is $1.5$.

Which of the following expression is correct for :

Taking the rays as incident from a medium of refractive index  $n_1$  to another of refractive index  $n_2$

The image obtained with a convex lens is erect and its length is four times the length of the object. If the focal length of the lens is $20 \mathrm{cm}$, the object and image distances are

A hollow double concave lens is made of very thin transparent material. It can be filled with air or either of two liquids $L_1$ or $L_2$ having refractive indices ${\mu }_1$ and ${\mu }_2$ respectively $\left({\mu }_2>{\mu }_1>1\right).$ The lens will diverge a parallel beam of light if it is filled with

A concave lens of glass, having refractive index $1.5,$ has both surfaces of same radius of curvature $R$. On immersion in a medium of refractive index $1.75,$ it will behave as a

What is focal length?

The radius of curvature of each surface of a convex lens having refractive index $1.8$ is $20 \mathrm{cm}$. The lens is now immersed in a liquid of refractive index $1.5$. The ratio of power of lens in air to its power in the liquid will be $x: 1$. The value of $x$ is

A bi convex lens of focal length $10 \mathrm{cm}$ is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is _____ $\mathrm{D}$.

A parallel beam of light enters a medium through convex interface as shown. Find the distance at which the rays converge

The power of a lens (biconvex) is $1.25 {\mathrm{m}}^{-1}$ in particular medium. Refractive index of the lens is $1.5$ and radii of curvature are $20 \mathrm{cm}$ and $40 \mathrm{cm}$ respectively. The refractive index of surrounding medium:
 

A thin equiconvex lens is made of glass of refractive index $1.5$ and its focal length in air is $0.2$ m. If it acts as a concave lens of $0.5 \mathrm{m}$ focal length when dipped in a liquid, the velocity of light in the liquid is
 

A convex lens of refractive index $1.5$ is immersed in a liquid of refractive index $1.6$ The lens will behave as a

The optical power of a lens is $\rho$ in air. Its optical power in a liquid of R.I.$= \mu$ is

Focal length of a convex lens will be maximum for