When an object is placed infront of a convex mirror at a distance ' $u$ ' from the pole of the mirror such that the size of the image is ' $n$ ' times that of the object. Then, the object distance ' $u=$

The ratio of the focal lengths of a convex lens when kept in air and when it is immersed in a liquid is $1: 2$. If the refractive index of the material of the lens is 1.5 , then the refractive index of the liquid is

If the least distance of distinct vision for a boy is 35 cm , then the lens to be used by the boy for correcting the defect of his eye is

A light ray falls on a rectangular glass slab as shown in the figure. If total internal reflection occurs at the vertical face of the slab at point $B$, the refractive index of glass is

Images of same size are formed by a convex lens when an object is placed either at 20 cm or 10 cm distance from the lens. The focal length of the lens is

A light ray incidents on an equilateral prism made of material of refractive index $\sqrt{3}$. Inside the prism, if the light ray moves parallel to the base of the prism, then the angle of incidence of the light ray is

Two thin convex lenses are kept in contact coaxially. If the focal length of the combination of the lenses is 4 cm and sum of the focal lengths of the two lenses is 18 cm , then the focal length of the lens of low power is

If the far point of a short sighted person is 400 cm , then the power of the lens required to enable him to see very distant objects clearly is

When a convex lens is immersed in a liquid of refractive index equal to $80 \%$ of the refractive index of the material of the lens. The focal length of the lens increases by $100 \%$. The refractive index of the liquid is

A needle is lying at the bottom of a water tank of height 12 cm. The apparent depth of the needle measured by a microscope is 9 cm . If the water is replaced by a liquid of refractive index of 1.5 of same height, the distance through which the microscope has to be moved to focus the needle again is

The radii of curvature of a double convex lens are 4 cm and 8 cm . If the refractive index of the material of the lens is 1.5 , the focal length of the lens is nearly.

A ray is incident from a medium of refractive index 2 into a medium of refractive index 1. The critical angle is

Assertion (A) The focal length of lens doesnot change when red light is replaced by bluelight.

Reason (R) The focal length of lens does notdepend on colour of light used.

Light of wavelength $$300 \mathrm{~nm}$$ in medium $$A$$ enters into medium $$B$$ through a plane surface. If the frequency of light is $$5 \times 10^{14} \mathrm{~Hz}$$ and the ratio of speed in medium $$A$$ to that in medium $$B$$ is $$4 / 5$$, the absolute refractive index of medium $$B$$ is