A ray of light passes from vacuum into a medium of refractive index \[\mu ,\] the angle of incidence is found to be twice the angle of refraction. Then the angle of incidence is
A vertical microscope is focused on a point at the bottom of an empty tank. Water \[\left( \mu =\frac{4}{3} \right)\] is then poured into the tank. The height of the water column is 4 cm. Another lighter liquid, which does not mix with water and which has refractive index \[\frac{3}{2}\] is then poured over the water. The height of liquid column is 2 cm. What is the vertical distance through which the microscope must be moved to bring the object in focus again?
A prism of dispersive power 0.021 and refractive index 1.53 form an achromatic combination with prism of angle \[4.2{}^\circ \] and dispersive power 0.045 having refractive index 1.65. Find the resultant deviation.
A ray incident at a point at an angle of incidence of \[{{60}^{o}},\] enters a glass sphere of refractive index \[n=\sqrt{3}\] and is reflected and refracted at the further surface of the sphere. The angle between the reflected and refracted rays at this surface is
A glass prism is immersed in a hypothetical liquid. The curves showing the refractive index n as a function of wavelength \[\lambda \] for glass and liquid are as shown in the figure. A ray of white light is incident on the prism parallel to the base. Choose the incorrect statement -
A horizontal ray of light passes through a prism of \[\mu =1.5\] whose apex angle is \[4{}^\circ \] and then strikes a vertical mirror M as shown. For the ray after reflection to become horizontal, the mirror must be rotated through an angle of:
A light wave travels from glass to water. The refractive index for glass and water are \[\frac{3}{2}\] and \[\frac{4}{3}\] respectively. The value of the critical angle will be:
A cylinderical optical fibre (quarter circular shape) of refractive index \[n=2\] and diameter \[d=4\text{ }mm\] is surrounded by air. A light beam is sent into the fibre along its axis as shown in figure. Then the smallest outer radius R (as shown in figure) for which no light escapes after first incident on curved surface of fibre is:
The refractive index of air is 1.0003. The thickness of air column which will have one more wavelength of yellow light \[(X=\text{ }6000\overset{o}{\mathop{A}}\,)\] than in the same thickness in vacuum is
A light beam is travelling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are \[{{n}_{0}},\,\frac{{{n}_{0}}}{2},\,\frac{{{n}_{0}}}{6}\] and \[\frac{{{n}_{0}}}{8},\] respectively. The angle of incidence 6 for which the beam just misses entering Region IV is
In the figure [a] the light is incident at an angle \[{{\mu }_{k}}=1-\frac{1}{{{n}^{2}}}\] (slightly greater than the critical angle). Now keeping the incident ray fixed a parallel slab of refractive index \[{{n}_{3}}\] is placed on surface AB.
A)
total internal reflection occurs at AB for \[{{n}_{3}}={{n}_{2}}\]
doneclear
B)
total internal reflection occurs at AB for \[{{n}_{3}}>{{n}_{1}}\]
doneclear
C)
the ray will return back to the same medium for all values of \[{{n}_{3}}\]
doneclear
D)
total reflection occurs at CD for \[{{n}_{3}}<{{n}_{1}}\].
A beam of monochromatic light is incident at \[i={{50}^{o}}\] on one face of an equilateral prism the angle of emergence is \[40{}^\circ ,\] then the angle of minimum deviation is-
r and r? denote the angles inside an equilateral prism, as usual, in degrees. Consider that during some time interval from \[t=0\] to \[t=t,\,r'\] varies with time as \[r'=10+{{t}^{2}}.\] During this time r will vary as: (Assume that r and r? are in degree):
One of the refracting surface of a prism of refractive index \[\sqrt{2}\] is silvered. The angle of the prism is equal to the critical angle of a medium of refractive index 2. A ray of light incident in the silvered surface passes through the prism and retraces its path after reflection at the silvered face. Then the angle of incidence on the un silvered surface is
A plane mirror is made of glass slab \[({{\mu }_{g}}=1.5)\,2.5\,\text{cm}\] thick and silvered on the back. A point object is placed 5 cm in front of the unsilvered face of the mirror. What will be the position of final image:
A transparent solid cylindrical rod has a refractive index of \[\frac{2}{\sqrt{3}}\]. It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure.
The incident angle \[(\theta )\] for which the light ray grazes along the wall of the rod is:
A ray hits the y-axis making an angle \[\theta \] with y-axis as shown in the figure. The variation of refractive index with x-coordinate is \[\mu ={{\mu }_{0}}\left( 1-\frac{x}{d} \right)\] for \[0\le \times \le d\left( 1-\frac{1}{{{\mu }_{0}}} \right)\] and \[\mu ={{\mu }_{0}}\] for \[x<0\] where d is a positive constant. The maximum x-coordinate of the path traced by the ray is
An isosceles trapezium of reflecting material of refractive index \[\sqrt{2}\] and dimension of sides being 5 cm, 5 cm, 10 cm and 5 cm. The angle of minimum deviation by this when light is incident from air and emerges in air is:
A man is standing at the edge of a 1 m deep swimming pool, completely filled with a liquid of refractive index \[\sqrt{3/2}\]. The eyes of the man are \[\sqrt{3}m\] above the ground. A coin located at the bottom of the pool appears to be at an angle of depression of \[\text{3}0{}^\circ \] with reference to the eye of man. Then horizontal distance (represented by \[\times \] in the figure) of the coin from the eye of the man is ..... mm.
Statement-1: Beam of white light is incident on a transparent glass hemisphere as shown in figure. The beam is rotated clockwise so that angle \[\theta \] increases, as the refracted beam approaches a direction parallel to the horizontal it appears red.
Statement-2: Critical angle for a pair of medium depends on \[Rl's\] of mediums and given by \[{{i}_{c}}={{\sin }^{-1}}\left( \frac{1}{_{R}{{\mu }_{D}}} \right)\And Rl\] in turn depends on wavelength of light.
A)
Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
doneclear
B)
Statement-1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for Statement-1
A point source of light is placed at a distance h below the surface of a large deep lake. What is the percentage of light energy that escapes directly from the water surface if \[\mu \] of water \[=\frac{4}{3}\]?
If the signal is transmitted from an optical fibre core of Refractive Index (RI) \[\sqrt{\frac{12}{5}}\] to an another optical fibre with RI of core and cladding as 1.8 and 1.2 respectively, then the maximum angle of acceptance for 2nd optical fibre is
A man in an empty swimming pool has a telescope focused at 4'O clock sun. When the swimming pool is filled with water, the man (now inside the water with his telescope undisturbed) observes the setting sun. Find the refractive index of water, if sun rises and sets at 6'O clock.
If \[{{\mu }_{1}}\] and \[{{\mu }_{2}}\] are the refractive indices of the materials of core and cladding of an optical fibre, then the loss of light due to its leakage can be minimised by having
A glass slab of width 't', refractive index \['\mu '\] is placed as shown in the figure. If the point object, moves with a speed 2 cm/sec towards the slab the observed speed by the observer will be :
Light is incident normally on face AB of a prism as shown in figure. A liquid of refractive index 3/2 is placed on face AC of the prism. The prism is made of glass of refractive index 3/2. The limits of \[\mu \]for which total internal reflection cannot take place on face AC is
A glass slab has the left half of refractive index \[{{n}_{1}},\] and the right half of \[{{n}_{2}}=3{{n}_{1}}\]. The effective refractive index of the whole slab is
Let the \[x-y\] plane be the boundary between two transparent media. Medium 1 in \[z\ge 0\] has refractive index of \[\sqrt{2}\] and medium 2 with \[z<0\] has a refractive index of \[\sqrt{3}\]. A ray of light in medium 1 given by the vector \[\vec{A}=6\sqrt{3}\hat{i}+8\sqrt{3}\,\hat{j}-10\hat{k}\] is incident on the plane of separation. The angle of refraction in medium 2 is