Ray Optics

A double convex lens made of glass of refractive index 1.5 and radii of curvature of the curved surfaces 20 cm each is immersed in a liquid of refractive index $n_L$. The correct plot showing the variation of the power, in the units of diopter $(D)$, as a function of $n_L$ is:

In the List-I, four optical effects are mentioned. The physical phenomena of light which are essential to describe these optical effects are given in List-II. Choose the option which describes the correct match between the entries in List-I to those in List-II.

A beam of polychromatic light passes through a thin prism of prism angle $6^\circ$. The refractive index of the material of the prism varies with wavelength $(\lambda)$ as $n(\lambda)=\alpha\lambda+\dfrac{\beta}{\lambda^2}$, where $\alpha=3\ \mu\text{m}^{-1}$ and $\beta=0.096\ \mu\text{m}^2$. If $\lambda_{\min}$ is the wavelength at which the angle of minimum deviation $D_m$ is smallest, then the correct value of $D_m$ at $\lambda_{\min}$ is

Consider two isosceles prisms 1 and 2 with prism angles $A_1$ and $A_2$ and refractive indices $n_1$ and $n_2$, respectively, as shown in the figure. The faces $a_1b_1$ and $a_2b_2$ are parallel to each other and perpendicular to the mirror $M$. If a ray of light is incident on the face $a_1c_1$ and emerges from the face $a_2c_2$, then the correct statement(s) is/are:

As shown in the figure, a ray $AB$ of unpolarized light enters from water of refractive index $n_w=4/3$ into a medium of refractive index $n_p=4/\sqrt3$ after passing through a glass plate of refractive index $n_g=1.5$ and a layer of water. At a particular incident angle $i$ the reflected ray $CD$ is polarized in the direction as shown in the figure. The value of $i$ (in degrees) is:

For a thin symmetric prism made of glass (refractive index 1.5), the ratio of incident angle and minimum deviation will be ________.

Refer the figure given below. $\mu_1$ and $\mu_2$ are refractive indices of air and lens material. The height of image will be ________ cm.

One side of an equilateral prism is painted by a transparent material of refractive index $n_2$. The refractive index of prism is 1.6. The minimum value of $n_2$ required for total internal reflection from painted face is ________.

If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at 30 cm above the paper. If the radius of curvature of the lens is 60 cm then the refractive index of the lens material is $\dfrac\alpha{10}$. The value of $\alpha$ is ________.

A rod of length 10 cm lies along the principle axis of a concave mirror of focal length 10 cm as shown in figure. The length of the image is ________ cm.

A telescope with objective diameter $R$ is used to observe a distant star emitting light of wavelength 500 nm, at a resolution of $5\times10^{-7}$ radian. The value of $R$ is ________ cm.

A convex lens is made from glass material having refractive index of 1.4 with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is ________.

A ray of light passing through an equilateral prism is having velocity $2.12\times10^8$ m/s in the prism material, then the minimum angle of deviation is ________ degrees.

A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of original objective lens. To retain same magnification keeping the object distance unchanged, the tube length has to be

A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses ?

An object $AB$ is placed 15 cm on the left of a convex lens $P$ of focal length 10 cm. Another convex lens $Q$ is now placed 15 cm right of lens $P$. If the focal length of lens $Q$ is 15 cm, the final image is ________.

A spherical interface lens of radius $R$ separates two media of refractive indices 1 and 1.4 respectively as shown in the figure below. A point source is placed at a distance of $4R$ in front of spherical interface. The magnitude of the magnification of point source image is ________.

Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is ________.

A concave mirror of focal length 10 cm forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is ________ cm.

A thin biconvex lens is prepared from the glass ($\mu=1.5$) both curved surfaces of which have equal radii of 20 cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of ________ cm.