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Solve this :$3.\mathrm{In}\mathrm{the}\mathrm{diagram}\mathrm{shown},\mathrm{the}\mathrm{cylinder}\mathrm{has}\mathrm{height}2\mathrm{H}\mathrm{and}\mathrm{diameter}3\mathrm{H}.\mathrm{Initially},\mathrm{the}\mathrm{observer}\mathrm{can}\mathrm{just}\mathrm{see}\mathrm{the}\mathrm{upper}\mathrm{edge}\mathrm{of}\mathrm{the}\mathrm{board}.\mathrm{When}\mathrm{the}\mathrm{cylinder}\mathrm{has}\mathrm{been}\mathrm{completely}\mathrm{filled}\mathrm{by}\mathrm{a}\mathrm{liquid}\mathrm{of}\mathrm{refractive}\mathrm{index}\mathrm{\mu},\mathrm{the}\mathrm{observer}\mathrm{from}\mathrm{the}\mathrm{same}\mathrm{position}\mathrm{can}\mathrm{just}\mathrm{see}\mathrm{the}\mathrm{complete}\mathrm{board}.\mathrm{The}\mathrm{board}\mathrm{has}\mathrm{a}\mathrm{square}\mathrm{shape}\mathrm{with}\mathrm{dimensions}\mathrm{H}\mathrm{x}\mathrm{H}.\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{\mu}.\phantom{\rule{0ex}{0ex}}\left(\mathrm{A}\right)\raisebox{1ex}{$2.5$}\!\left/ \!\raisebox{-1ex}{$\sqrt{5}$}\right.\left(\mathrm{B}\right)\frac{2\sqrt{2}}{\sqrt{5}}\phantom{\rule{0ex}{0ex}}\left(\mathrm{C}\right)\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$\sqrt{5}$}\right.\left(\mathrm{D}\right)\mathrm{none}$

34.A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is emmersed in 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 brightspot of diameter 11.54 mm on the top of the block. The refractive index of the liquid is[JEE Advance - 2014]40.A monochromatic beam of light is incident at 60$\xb0$ on one face of an equilateral prism of refractive intex n and emerges from the opposite face making an angle $\theta $(n) with the normal (see the figure). For n = $\sqrt{3}$ the value of $\theta $ is 60$\xb0$ and $\frac{d\theta}{dn}=m.$The value of m is[JEE Advane - 2015]37.Two identical glass rods S_{1}and S_{2}(refractive Index. 1.5) have one convex end of radius of curvatur 10 cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light P is placed inside rod S_{1}, on its axis at a distance of 50 cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside S_{2}. the distance d is[JEE Advance - 2015](A) 60 cm (B) 70 cm (C) 80 cm (D) 90 cmQ1. Light from a laser is directed at a hemi-spherical glass. The light passes undeviated through the block and on to a screen, forming a spot as shown. The semi-circular block is rotated about an axis perpendicular to plane of paper through point P. The spot of light on the screen is seen to move downwards. When the spot reaches point B, it disappears. In a particular experiment, the distance PA is 120 cm and distance AB is 90 cm. Calculate the refractive index of the glass of the block.

$\left(\mathrm{A}\right)\frac{5}{3}\left(\mathrm{B}\right)\frac{5}{4}\left(\mathrm{C}\right)\frac{4}{3}\left(\mathrm{D}\right)\mathrm{None}\mathrm{of}\mathrm{these}$

7.If an object is placed at A (OA > f); Where f is the focal length of the lens the image is found to be formed at B. A perpendicular is erected at O and C is chosen on it such that the angle $\angle $BCA is a right angle. Then the value of f will be (A) AB/OC^{2}(B) (AC)(BC)/OC(C) (OC)(AB)/AC+BC (D) OC

^{2}/ABa) 10 cm

b) 20 cm

c) 40 cm

d) infinity

Q36. 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 fo light traversing from glass to air get focused at distance f_{2}from the film. Then(A) |f

_{1}| = 3 R(B) |f

_{1}| = 2.8 R(C) |f

_{2}| = 2 R(D) |f

_{2}| = 1.4 RGiven lamda= 5.5x10^-7 m, which is true:

a) Yes possible with same aperture size

b) no, not possible

c) possible also when aperture half of present diameter

d) Data not sufficient.

12.Light from a luminous point on the lower face of a 2 cm thick glass slab, strikes the upper face and the totally reflected rays outline a circle of radius 3.2 cm on the lower face. What is the refractive index of the glass.(A) 1.5

(B) 1.6

(C) 1.7

(D) 1.8

11. A point source of light is 60 cm from a screen and it kept at the focus of a concave mirror which reflects light on the screen. The focal length of the mirror is 20 cm. The ratio of average intensities of the illumination on the screen when the mirror is present and when the mirror is removed is:

(A) 36:1 (B) 37:1 (C) 49:1 (D) 10:1

10.A ray incident at an angle 53$\xb0$ on a prism emerges at an angle at 37$\xb0$ as shown. If the angle of incidence is made 50$\xb0$, which of the following is a possible value of the angle of emergence.(A) 35$\xb0$ (B) 42$\xb0$ (C) 40$\xb0$ (D) 38$\xb0$

Q. For two structures namely S

_{1}with n_{1}= $\frac{\sqrt{45}}{4}$ and n_{2}= $\frac{3}{2},\mathrm{and}{\mathrm{S}}_{2}\mathrm{with}{\mathrm{n}}_{1}=\frac{8}{5}\mathrm{and}{\mathrm{n}}_{2}=\frac{7}{5}$ and taking the refractive index of water to be 4/3 and that of air to be 1, the correct option (s) is (are)(A) NA of S

_{1}immersed in water is the same as that of S_{2}immersed in a liquid of refractive index $\frac{16}{3\sqrt{15}}$(B) NA of S

_{1 }immersed in liquid of refractive index $\frac{6}{\sqrt{15}}$ is the same as that of S_{2}immersed in water(C) NA of S

_{1}placed in air is the same as that of S_{2}immersed in liquid of refractive index $\frac{4}{\sqrt{15}}$(D) NA of S

_{1}placed in air is the same as that of S_{2}placed in water37. The x-y plane is the boundary between two transparent media. Medium -1 with z>0 has refractive index $\sqrt{2}$ and medium -2 with z<0 has a refractive index $\sqrt{3}$. A ray of light in medium -1 gien by the vector $\mathrm{A}=6\sqrt{3}\hat{\mathrm{i}}+8\sqrt{8}\hat{\mathrm{j}}-10\hat{\mathrm{k}}$ is incident on the plane of separation. Find the unit vector in the direction of refracted ray in medium -2

(A) the minimum magnifcation is 20 and corresponds to the separation 9.8 cm between lenses.

(B) the minimum magnifcation is 20 and corresponds to the separation 11.8 cm between lenses.

(C) the minimum magnifcation is 30 and corresponds to the separation 9.8 cm between lenses.

(D) the minimum magnifcation is 30 and corresponds to the separation 11.8 cm between lenses.

The distance of an object from the principal focus of a concave mirror of focal length F is D. The ratio of the size of image to the size of object is

a) F/D

b) (F/D)

^{2}c) (F/D)

^{1/2}d) F+D/F-D

37. The x-y plane is the boundary between two transparent media. Medium -1 with z>0 has refractive index $\sqrt{2}$ and medium -2 with Z<0 has a refractive index $\sqrt{3}$. A ray of light in medium -1 given by the vector $\mathrm{A}=6\sqrt{3}\hat{\mathrm{i}}+8\sqrt{3}\hat{\mathrm{j}}-10\hat{\mathrm{k}}$ is incident on the plane of separation. Find the unit vector in the direction on refracted ray in medium -2.

reply asap plz

1. A ray incident at point B at an angle of incidence $\theta $ enters into a glass sphere and is reflected and refracted at the farther surface of the sphere, as shown. The angle between the reflected and refracted rays at this surface is 90$\xb0$ . If refractive index of material of sphere is $\sqrt{3},$ the value of $\theta $ is

$a)\mathrm{\pi}/3\mathrm{b})\mathrm{\pi}/4\mathrm{c})\mathrm{\pi}/6\mathrm{d})\mathrm{\pi}/12$

2. Light in incident from glass $\left(\mu =1.5\right)$ to water $\left(\mu =\frac{4}{3}\right)$. Find the range of deviation for which there are two angle of incidence.

$a){\mathrm{sin}}^{-1}(8/9)to\mathrm{\pi}/2\mathrm{b})0\mathrm{to}{\mathrm{sin}}^{-1}(8/9)\mathrm{c})0\mathrm{to}{\mathrm{cos}}^{-1}(8/9)\mathrm{d}){\mathrm{cos}}^{-1}\left(8/9\right)\mathrm{to}\mathrm{\pi}/2$

12. What will be the minimum angle of incident such that the total internal reflection occurs on both the surfaces ?

Q.10. How much water would be filled in a container of height 21 cm, so that it appears half filled to the observer when viewed from the top of the container? (${\mu}_{W}$ = 4/3)

Prove that :-

Length of AB is independent of angles.

Q10. A simple telescope consisting of an objective of focal length 60 cm and a single eye lens of focal length 5 cm is focussed on a distant object in such a way that parallel rays emerge from eye lens. If the object subtends an angle of 20 at the objective, the angular width of the image is

(A) 100 (B) 240 (C) 500 (D) (1/6)0

Q.52. A prism has a refractive index $\sqrt{\frac{3}{2}}$ and refracting angle 90$\xb0$. Find the minimum deviation produced by prism

(A) 40$\xb0$

(B) 45$\xb0$

(C) 30$\xb0$

(D) 49$\xb0$

andn_{1}n_{2 in the formulae of refraction at spherical surface}Column I

(A) A ray is falling on a plane smooth mirror

(B) A ray is going from a rarer to denser medium

(C) A ray is going from a denser to rarer medium

(D) A ray is falling on a prism