Ray Optics

A light ray is incident, at an incident angle $\theta_1$, on the system of two plane mirrors $M_1$ and $M_2$ having an inclination angle 75° between them (as shown in figure). After reflecting from mirror $M_1$ it gets reflected back by the mirror $M_2$ with an angle of reflection 30°. The total deviation of the ray will be ______ degree.

A small bulb is placed at the bottom of a tank containing water to a depth of $\sqrt7$ m. The refractive index of water is $\dfrac43$. The area of the surface of water through which light from the bulb can emerge out is $x\pi$ m$^2$. The value of $x$ is ______.

Consider a light ray travelling in air is incident into a medium of refractive index $\sqrt{2n}$. The incident angle is twice that of refracting angle. Then, the angle of incidence will be :

A convex lens has power P. It is cut into two halves along its principal axis. Further one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figures). Choose the incorrect option for the reported pieces.

If a wave gets refracted into a denser medium, then which of the following is true?

The refracting angle of a prism is A and refractive index of the material of the prism is $\cot(A/2)$. Then the angle of minimum deviation will be -

A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30 cm and refractive index 1.5. The distance from the centre of the globe at which the beam of light can converge is ______ mm.

The speed of light in media 'A' and 'B' are $2.0\times10^{10}$ cm/s and $1.5\times10^{10}$ cm/s respectively. A ray of light enters from the medium B to A at an incident angle '$\theta$'. If the ray suffers total internal reflection, then

The refractive index of an equilateral prism is $\sqrt2$. The angle of emergence under minimum deviation position of prism, in degree, is ______.

Which of the following statement is correct ?

Time taken by light to travel in two different materials A and B of refractive indices $\mu_A$ and $\mu_B$ of same thickness is $t_1$ and $t_2$ respectively. If $t_2-t_1=5\times10^{-10}$ s and the ratio of $\mu_A$ to $\mu_B$ is 1 : 2. Then, the thickness of material, in meter is : (Given $v_A$ and $v_B$ are velocities of light in A and B materials respectively.)

For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm form the lens. A glass plate of refractive index 1.5 and thickness 1 cm is introduced between lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screeen ?

A convex lens of focal length 20 cm is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is ______ cm.

The graph between $\dfrac1u$ and $\dfrac1v$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is 1.5 and its both the surfaces have same radius of curvature R. The value of R will be ______ cm.

(where $u$ = object distance, $v$ = image distance)

Light travels in two media $M_1$ and $M_2$ with speeds $1.5\times10^8$ ms$^{-1}$ and $2.0\times10^8$ ms$^{-1}$ respectively. The critical angle between them is :

In the given figure, the face AC of the equilateral prism is immersed in a liquid of refractive index 'n'. For incident angle 60° at the side AC, the refracted light beam just grazes along face AC. The refractive index of the liquid $n=\dfrac{\sqrt x}4$. The value of $x$ is ______.

(Given refractive index of glass = 1.5)

A thin prism of angle 6° and refractive index for yellow light $(n_Y)$ 1.5 is combined with another prism of angle 5° and $n_Y=1.55$. The combination produces no dispersion. The net average deviation (δ) produced by the combination is $\left(\dfrac1x\right)^\circ$. The value of $x$ is ______.

In normal adjustment, for a refracting telescope, the distance between objective and eye piece is 30 cm. The focal length of the objective, when the angular magnification of the telescope is 2, will be :

The power of a lens (biconvex) is 1.25 m$^{-1}$ in particular medium. Refractive index of the lens is 1.5 and radii of curvature are 20 cm and 40 cm respectively. The refractive index of surrounding medium:

An object 'o' is placed at a distance of 100 cm in front of a concave mirror of radius of curvature 200 cm as shown in the figure. The object starts moving towards the mirror at a speed 2 cm/s. The position of the image from the mirror after 10 s will be at ______ cm.