Geometrical Optics

A ray of light travelling in air is incident on one face of a parallel glass slab of thickness $t$ and refractive index $\mu$ at an angle of incidence $i$ ．Total time spent by the ray inside the slab is

An electromagnetic wave，whose wave normal makes an angle of $45^{\circ}$ with the vertical，is travelling in air and strikes a horizontal liquid surface．While travelling through the liquid，it gets deviated by $15^{\circ}$ ．If the speed of el...

A plano－convex lens fits exactly into a plano－concave lens．Their plane surfaces are parallel to each other．If lenses are made of different materials of refractive indices $\mu_1$ and $\mu_2$ and $R$ is the radius of curvature of the curved ...

A person has a minimum distance of distinct vision of 50 cm ．The power of lenses required to read a book at a distance of 25 cm is

Figure shows the graph of angle of deviation $\delta$ versus angle of incidence i for a light ray striking a prism. The prism angle is

Two convex lens \((\mathrm{L}_1\) and \(\mathrm{L}_2)\) of equal focal length \(\mathrm{f}\) are placed at a distance \(\frac{\mathrm{f}}{2}\) apart. An object is placed at a distance \(4 \mathrm{f}\) in the left of \(\mathrm{L_1}\) as show...

If \(\hat{n}_1, \hat{n}_2\) and \(\hat{\mathrm{t}}\) represent, unit vectors along the incident ray, reflected ray and normal to the surface respectively, then

When a convex lens is placed above an empty tank, the image of a mark at the bottom of the tank, which is 45 cm from the lens is formed 36 cm above the lens. When a liquid is poured in the tank to a depth of 40 cm, the distance of the image...

Three identical convex lenses each of focal length \(\mathrm{f}\) are placed in a straight line separated by a distance \(\mathrm{f}\) from each other. An object is located at f/2 in front of the leftmost lens. Then,

The human eye has an approximate angular resolution of \(\theta\) = 5.8 \(\times\) 10\(-\)4 rad and typical photo printer prints a minimum of 300 dpi (dots per inch, 1 inch = 2.54 cm). At what minimal distance d should a printed page be hel...

The cross-section of a reflecting surface is represented by the equation x2 + y2 = R2 as shown in the figure. A ray travelling in the positive x-direction is directed toward positive y-direction after reflection from the surface at point M....

A spherical convex surface of power 5 D separates object and image space of refractive indices 1.0 and \(4\over3\) , respectively. The radius of curvature of the surface is

A thin convex lens is placed just above an empty vessel of depth 80 cm. The image of a coin kept at the bottom of the vessel is thus formed 20 cm above the lens. If now water is poured in the vessel upto a height of 64 cm, what will be the ...

A tennis ball hits the floor with a speed v at an angle \(\theta\) with the normal to the floor. If the collision is inelastic and the coefficient of restitution is \(\varepsilon\), what will be the angle of reflection?

An object, is placed 60 cm in front of a convex mirror of focal length 30 cm. A plane mirror is now placed facing the object in between the object and the convex mirror such that it covers lower half of the convex mirror. What should be the...

A ray of light is reflected by a plane mirror. \({\widehat e_0}\), \(\widehat e\) and \(\widehat n\) be the unit vectors along the incident ray, reflected ray and the normal to the reflecting surface respectively.Which of the following give...

A point object is placed on the axis of a thin convex lens of focal length 0.05 m at a distance of 0.2 m from the lens and its image is formed on the axis. If the object is now made to oscillate along the axis with a small amplitude of A cm...

A ray of light is incident on a right angled isosceles prism parallel to its base as shown in the figure. Refractive index of the material of the prism is \(\sqrt 2\). Then, which of the following statement(s) is/are true?

A point source is placed at coordinates (0, 1) in xy-plane. A ray of light from the source is reflected on a plane mirror placed along the X-axis and perpendicular to the xy-plane. The reflected ray passes through the point (3, 3). What is ...

Two identical equiconvex lenses, each of focal length f are placed side by side in contact with each other with a layer of water in between them as shown in the figure. If refractive index of the material of the lenses is greater than that ...

There is a small air bubble at the centre of a solid glass sphere of radius r and refractive index \(\mu\). What will be the apparent distance of the bubble from the centre of the sphere, when viewed from outside?

A parallel beam of light is incident on a glass prism in the shape of a quarter cylinder of radius R = 0.05 m and refractive index n = 1.5, placed on a horizontal table as shown in the figure. Beyond the cylinder, a patch of light is found ...

The ratio of the diameter of the sun to the distance between the earth and the sun is approximately 0.009. The approximate diameter of the image of the sun formed by concave spherical mirror of radius of curvature 0.4 m is

A point object is held above a thin equiconvex lens at its focus. The focal length is 0.1 m and the lens rests on a horizontal thin plane mirror. The final image will be formed at

A ray of light strikes a glass plate at an angle of 60\(^\circ\). If the reflected and refracted rays are perpendicular to each other, the refractive index of glass is

Light travels through a glass plate of thickness t and having refractive index \(\mu\). If c be the velocity of light in vacuum, time taken by the light to travel through this thickness of glass is

A point source of light is kept at a depth of h in water of refractive index 4/3. The radius of the circle at the surface of water through which light emits is

The radius of curvature of a concave mirror is 24 cm and the image is magnified by 1.5 times. The object distance is

The refractive indices of glass and quartz w.r.t. air are 3/2 and 12/5 respectively. The refractive index of quartz w.r.t. glass is