Refraction at Plane Surfaces

The reason for using lead glass in the preparation of lenses is ,it is

A ray of light moving along the unit vector $(–\hat{\mathrm{i}}–2\hat{\mathrm{j}})$ undergoes refraction at an interface of two media, which is the $x-z$ plane. The refractive index for $y>0$ is $2$ while for $y<0$, it is $\frac{\sqrt{5}}{2}$ . The unit vector along which the refracted ray moves is 

A parallel sided block of glass of refractive index $1.5$ which is $3.6 \mathrm{mm}$ thick rests on the floor of a tank which is filled with water (refractive index$=\frac{4}{3}$). The difference between the apparent depth of floor at $A$ and $B$ when seen from vertically above is equal to

A ray of sunlight enters a spherical water droplet ($n =\frac{4}{3}$) at an angle of incidence $53°$ measured with respect to the normal to the surface. It is reflected from the back surface of the droplet and re-enters into the air. The angle between the incoming and outgoing ray is [Take $\sin 53° = 0.8$]

A surveyor on one bank of canal observed the image of the 4 inch and 17 ft marks on a vertical staff, which is partially immersed in the water and held against the bank directly opposite to him, coincides. If the 17 ft mark and the surveyor's eye are both 6 ft above the water level, If the width of the canal is 10 + x, assuming that the refractive index of the water is 4/3, then find the value of x. Zero mark is at the bottom of the canal.

A surveyor on one bank of canal observed the image of the 4 inch and 17 ft marks on a vertical staff, which is partially immersed in the water and held against the bank directly opposite to him, coincides. If the 17 ft mark and the surveyor's eye are both 6 ft above the water level, If the width of the canal is 10 + x, assuming that the refractive index of the water is 4/3, then find the value of x. Zero mark is at the bottom of the canal.

A beam of parallel rays of width b propagates in glass at over to air this face is _________  if the refractive index of glass is μ.v

When light travels from a rarer to a denser medium, which of the following parameter of light decreases:

A ray of light passes through four transparent media with refractive indices ${\mu }_1, {\mu }_2, {\mu }_3$ and ${\mu }_4$ as shown in the figure. The surfaces of all media are parallel. If the emergent ray $CD$ is parallel to the incident ray $AB$, we must have

A diverging beam of light from a point source S  having divergence angle  $\alpha$ , falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is

A monochromatic beam of light of wavelength $6000 Å$ in vacuum enters a medium of refractive index $1.5$. In the medium its wavelength is __________, its frequency is ____________

When a ray of light enters a glass slab from air

A light of wavelength $6000\mathrm{\AA }$ in air, enters a medium with refractive index $1.5$. Inside the medium its frequency is $5\times {10}^{14} \mathrm{Hz}$ and its wavelength is_______ $\mathrm{\AA }$.

If ${\epsilon }_0$ and ${\mu }_0$ are, respectively, the electric permittivity and magnetic permeability of free space, $\epsilon$ and $\mu$ the corresponding quantities in a medium, the index of refraction of the medium in terms of the above parameters is

A light wave of frequency  $5\times 10^{14} \mathrm{Hz}$ enters a medium of refractive index $1.5$. In the medium the velocity of the light wave is ________________ and its wavelength is ______________

In the given figure, a ray of light falls obliquely on a vertical glass slab and after refraction from slab falls on a vertical plane mirror at an angle $x$. the value of $x$ is

In the diagram as shown, a light ray is incident on the lower medium boundary at an angle$45°$ with the normal. Which of the following statements is/are correct?

A transparent sphere of radius $R$ has a cavity of radius $\frac{R}{2}$ as shown in figure. Find the refractive index of the sphere if a parallel beam of light falling on left surface focuses at point $P$.

As shown in the figure, a plane mirror is fixed at a height of $50 \mathrm{cm}$ from the bottom of tank containing water $\left(\mu =\frac{4}{3}\right)$. The height of water in the tank is $8 \mathrm{cm}$. A small bulb is placed at the bottom of the water tank. The distance of image of the bulb formed by mirror from the bottom of the tank is  ______ $\mathrm{cm}$.