Reflection of Light

Back surface of a glass (refractive index $n$ and thickness $t$) is polished to work as a mirror as shown below. A laser beam falls on it and is partially reflected and refracted at the air-glass interface and fully reflected at the mirror surface, respectively. A pattern of discrete spots of light is observed on the screen.

The spacing between the spots on the screen will be

When a light ray after suffering any number of reflections and refractions, its final path has reversed, it travels back along its entire initial path.

Refractive index of a medium depend upon the temperature of the medium.

A monochromatic beam of light enters a square enclosure with mirrored interior surfaces at an angle of incidence ${\theta }_i=(\ne 0)$ (see the figure below). For some value(s) of ${\theta }_i$, the beam is reflected by every mirrored wall (other than the one with opening) exactly once and exists the enclosure through the same hole. Which of the following statements about this beam is correct?

A ray of light travelling in the direction $\frac{1}{2}(\hat{\mathrm{i}}+\sqrt{3}\hat{\mathrm{j}})$ is incident on a plane mirror. After reflection, it travels along the direction $\frac{1}{2}(\hat{\mathrm{i}}-\sqrt{3\hat{\mathrm{j}}}).$ The angle of incidence is:

The image of an object $O$ due to reflection from the surface of a lake is elongated due to the ripples on the water surface caused by a light breeze. This is because the ripples act as tilted mirrors as shown below. Consider the case, where $O$ and the observer $E$ are at the same height above the surface of the lake. If the maximum angle that the ripples make with the horizontal is $\alpha$, then the angular extent $\delta$ of the image will be

A ray of light travelling in the direction $\frac{1}{2}(\widehat{i}+\sqrt{3}\widehat{j})$ is incident on a plane mirror. After reflection, it travels along the direction $\frac{1}{2}(\hat{i}-\sqrt{3}\hat{j})$ . The angle of incidence is 

A ray of light is incident at $50°$ on the middle of one of the two mirrors arranged at an angle of $60°$ between them. The ray then touches the second mirror, get reflected back to the first mirror, making an angle of incidence of

When diffuse reflection from a surface occurs

It is necessary to illuminate the bottom of a well by reflected solar beam when the light is incident at an angle of $\mathrm{\alpha }=40°\mathrm{ }$to the vertical. At what angle $\mathrm{\beta }\mathrm{ }$to the horizontal should a plane mirror be placed?

The principal section of a glass prism is an isosceles triangle $ABC$ with $AB=AC.$ The face $AC$ is silvered. A ray of light is incident normally on the face $AB$ and after tworeflections, it emerges from the base $BC$ perpendicular to the base. Angle $BAC$ of the prism is

A ray of light is incident on a plane mirror along the direction given by vector $\overrightarrow{A} = 2\mathbf{î} - 3\mathbf{ĵ}\mathbf{ }+ 4\hat{\text{k}}.$ Find the unit vector along reflected ray. Take normal to mirror along the direction of vector $\overrightarrow{B}= 3\mathbf{î}-6\mathbf{ĵ}+ 2\hat{\mathbf{k}}.$

The circular boundary of the concave mirror subtends a cone of half angle $\theta$ at its centre of curvature. The minimum value of $\theta$ for which ray incident on this mirror parallel to the principle axis suffers reflection more than once is

A ray of light strikes a plane mirror and gets reflected as shown in the adjoining diagram. If $\widehat{u}, \widehat{v}$ and $\widehat{n}$  are unit vectors along the incident ray, reflected ray and the normal respectively, then which of the following relation is correct?

A 1 m long mirror is placed at a distance $4 \mathrm{m}$ from a tall building as shown in the diagram. What height of the building can be seen in the mirror from a point $\mathrm{O}$ at a distance $2 \mathrm{m}$ from the mirror?