Ray Optics

A thin convex lens of focal length 'f' is put on a plane mirror as shown in the figure. When an object is kept at a distance 'a' from the lens - mirror combination, its image is formed at a distance $\dfrac a3$ in front of the combination. The value of 'a' is :

A transparent thin film of uniform thickness and refractive index $n_1=1.4$ is coated on the convex spherical surface of radius $R$ at one end of a long solid glass cylinder of refractive index $n_2=1.5$, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance $f_1$ from the film, while rays of light traversing from glass to air get focused at distance $f_2$ from the film. Then

A point source $S$ is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter 11.54 mm on the top of the block. The refractive index of the liquid is

Four combinations of two thin lenses are given in List I. The radius of curvature of all curved surfaces is $r$ and the refractive index of all the lenses is 1.5. Match lens combinations in List I with their focal length in List II and select the correct answer using the code given below the lists.

A thin convex lens made from crown glass $\left(\mu=\dfrac32\right)$ has focal length $f$. When it is measured in two different liquids having refractive indices $\dfrac43$ and $\dfrac53$, it has the focal lengths $f_1$ and $f_2$ respectively. The correct relation between the focal lengths is :

A green light is incident from the water to the air - water interface at the critical angle ($\theta$). Select the correct statement.

A diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is $\dfrac43$, and the diver's eyes are 15 cm below the surface of water. Then the radius of the circle is :

The focal lengths of objective lens and eye lens of a Gallelian Telescope are respectively 30 cm and 3.0 cm. Telescope produces virtual, erect image of an object situated far away from it at least distance of distinct vision from the eye lens. In this condition, the Magnifying Power of the Gallelian Telescope should be :

An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two positions of a thin lens separated by 10 cm. The size of the images in two situations are in the ratio 3 : 2. What is the distance between the screen and the object ?

In a compound microscope the focal length of objective lens is 1.2 cm and focal length of eye piece is 3.0 cm. When object is kept at 1.25 cm in front of objective, final image is formed at infinity. Magnifying power of the compound microscope should be :

The refractive index of the material of a concave lens is $\mu$. It is immersed in a medium of refractive index $\mu_1$. A parallel beam of light is incident on the lens. The path of the emergent rays when $\mu_1>\mu$ is :

Interference pattern is observed at 'P' due to superimposition of two rays coming out from a source 'S' as shown in the figure. The value of '$l$' for which maxima is obtained at 'P' is :

(R is perfect reflecting surface) :

A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is $\theta_{iC}$ and the Brewster's angle of incidence is $\theta_{iB}$, such that $\sin\theta_{iC}/\sin\theta_{iB}=\eta=1.28$. The relative refractive index of the two media is :

A ray of light travelling in the direction $\frac12\left(\hat i+\sqrt3\hat j\right)$ is incident on a plane mirror. After reflection, it travels along the direction $\frac12\left(\hat i-\sqrt3\hat j\right)$. The angle of incidence is

The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is $\dfrac23$ times the wavelength in free space. The radius of the curved surface of the lens is

A right angled prism of refractive index $\mu_1$ is placed in a rectangular block of refractive index $\mu_2$, which is surrounded by a medium of refractive index $\mu_3$, as shown in the figure. A ray of light '$e$' enters the rectangular block at normal incidence. Depending upon the relationships between $\mu_1$, $\mu_2$ and $\mu_3$, it takes one of the four possible paths '$ef$', '$eg$', '$eh$' or '$ei$'.

Match the paths in List I with conditions of refractive indices in List II and select the correct answer using the codes given below the lists:

A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index $n$ of the first lens is 1.5 and that of the second lens is 1.2. Both the curved surfaces are of the same radius of curvature $R=14$ cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be

For light incident from air on a meta-material, the appropriate ray diagram is

Choose the correct statement.

A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence $\theta$. The reflected (R) and transmitted (T) intensities, both as function of $\theta$, are plotted. The correct sketch is