Science (English Medium) Class 12 - CBSE Question Bank Solutions for Physics

Two transparent slabs having equal thickness but different refractive indices µ₁ and µ₂are pasted side by side to form a composite slab. This slab is placed just after the double slit in a Young's experiment so that the light from one slit goes through one material and the light from the other slit goes through the other material. What should be the minimum thickness of the slab so that there is a minimum at the point P₀ which is equidistant from the slits?

A thin paper of thickness 0.02 mm having a refractive index 1.45 is pasted across one of the slits in a Young's double slit experiment. The paper transmits 4/9 of the light energy falling on it. (a) Find the ratio of the maximum intensity to the minimum intensity in the fringe pattern. (b) How many fringes will cross through the centre if an identical paper piece is pasted on the other slit also? The wavelength of the light used is 600 nm.

A Young's double slit apparatus has slits separated by 0⋅28 mm and a screen 48 cm away from the slits. The whole apparatus is immersed in water and the slits are illuminated by red light \[\left( \lambda = 700\text{ nm in vacuum} \right).\] Find the fringe-width of the pattern formed on the screen.

A parallel beam of monochromatic light is used in a Young's double slit experiment. The slits are separated by a distance d and the screen is placed parallel to the plane of the slits. Slow that if the incident beam makes an angle \[\theta =  \sin^{- 1}   \left( \frac{\lambda}{2d} \right)\] with the normal to the plane of the slits, there will be a dark fringe at the centre P₀ of the pattern.

A double slit S₁ − S₂ is illuminated by a coherent light of wavelength \[\lambda.\] The slits are separated by a distance d. A plane mirror is placed in front of the double slit at a distance D₁ from it and a screen ∑ is placed behind the double slit at a distance D₂ from it (see the following figure). The screen ∑ receives only the light reflected by the mirror. Find the fringe-width of the interference pattern on the screen.

White coherent light (400 nm-700 nm) is sent through the slits of a Young's double slit experiment (see the following figure). The separation between the slits is 0⋅5 mm and the screen is 50 cm away from the slits. There is a hole in the screen at a point 1⋅0 mm away (along the width of the fringes) from the central line. (a) Which wavelength(s) will be absent in the light coming from the hole? (b) Which wavelength(s) will have a strong intensity?

Consider the arrangement shown in the figure. The distance D is large compared to the separation d between the slits. 

1. Find the minimum value of d so that there is a dark fringe at O.
2. Suppose d has this value. Find the distance x at which the next bright fringe is formed. 
3. Find the fringe-width.
   

A normal eye is not able to see objects closer than 25 cm because

In a Young's double slit experiment, the separation between the slits = 2.0 mm, the wavelength of the light = 600 nm and the distance of the screen from the slits = 2.0 m. If the intensity at the centre of the central maximum is 0.20 W m⁻², what will be the intensity at a point 0.5 cm away from this centre along the width of the fringes?

In a Young's double slit interference experiment, the fringe pattern is observed on a screen placed at a distance D from the slits. The slits are separated by a distance d and are illuminated by monochromatic light of wavelength \[\lambda.\] Find the distance from the central point where the intensity falls to (a) half the maximum, (b) one-fourth the maximum.

In a Young's double slit experiment, \[\lambda = 500\text{ nm, d = 1.0 mm and D = 1.0 m.}\] Find the minimum distance from the central maximum for which the intensity is half of the maximum intensity.

The line-width of a bright fringe is sometimes defined as the separation between the points on the two sides of the central line where the intensity falls to half the maximum. Find the line-width of a bright fringe in a Young's double slit experiment in terms of \[\lambda,\] d and D where the symbols have their usual meanings.

A thin converging lens is formed with one surface convex and the other plane. Does the position of image depend on whether the convex surface or the plane surface faces the object?

Consider the arrangement shown in the figure. By some mechanism, the separation between the slits S₃ and S₄ can be changed. The intensity is measured at the point P, which is at the common perpendicular bisector of S₁S₂ and S₂S₄. When \[z = \frac{D\lambda}{2d},\] the intensity measured at P is I. Find the intensity when z is equal to

(a) \[\frac{D\lambda}{d}\]

(b) \[\frac{3D\lambda}{2d}\]  and

(c) \[\frac{2D\lambda}{d}\]

A double convex lens has two surfaces of equal radii R and refractive index \[m = 1 \cdot 5\]

A symmetric double convex lens in cut in two equal parts by a plane perpendicular to the principal axis. If the power of the original lens was 4 D, the power a cut-lens will be

A symmetric double convex lens is cut in two equal parts by a plane containing the principal axis. If the power of the original lens was 4 D, the power of a divided lens will be

Consider three converging lenses L₁, L₂ and L₃ having identical geometrical construction. The index of refraction of L₁ and L₂ are \[\mu_1   \text{ and }   \mu_2\] respectively. The upper half of the lens L₃ has a refractive index \[\mu_1\] and the lower half has \[\mu_2\]  following figure . A point object O is imaged at O₁ by the lens L₁ and at O₂ by the lens L₂placed in same position. If L₃ is placed at the same place,

(a) there will be an image at O₁
(b) there will be an image at O₂.
(c) the only image will form somewhere between O₁ and O₂
(d) the only image will form away from O₂.

A screen is placed a distance 40 cm away from an illuminated object. A converging lens is placed between the source and the screen and its is attempted to form the image of the source on the screen. If no position could be found, the focal length of the lens

A double convex lens has focal length 25 cm. The radius of curvature of one of the surfaces is double of the other. Find the radii, if the refractive index of the material of the lens is 1.5.