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 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:
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 \[{{n}_{3}}<{{n}_{1}}\].
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):
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 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