Optics
- The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at 22.5^° from the polarization axis of one of the polaroid, is (I_0 is the intensity of polarised light after passing through the first polaroid): Answer: 3. I₀/8 Key idea: apply Malus's law, I=I₀cos²θ , at each polaroid. The middle sheet is at 22.5^° to the first, and 90^°-22.5^°=67.5^... 1
- An unpolarized light beam travelling in air is incident on a medium of refractive index 1.73 at Brewster's angle. Then- Answer: 1. reflected light is completely polarized and the angle of reflection is close to 60^° Key idea: at Brewster's angle tan i_B=μ , an... 1
- In a certain camera, a combination of four similar thin convex lenses are arranged axially in contact. Then the power of the combination and the total magnification in comparison to the power (p) and magnification (m) for each lens will be, respectiv… Answer: 3. 4p and m⁴ Key idea: powers of thin lenses in contact add, while magnifications of successive images multiply. Power: P=p+p+p+p=4p... 1
- A microscope has an objective of focal length 2 cm, eyepiece of focal length 4 cm and the tube length of 40 cm. If the distance of distinct vision of eye is 25 cm, the magnification in the microscope is Answer: 2. 125 Key idea: for a compound microscope, the magnification is the product of the objective magnification and the eyepiece magnifi... 1
- A small telescope has an objective of focal length 140 cm and an eye piece of focal length 5.0 cm. The magnifying power of telescope for viewing a distant object is: Answer: 3. 28 Key idea: For a telescope in normal adjustment (distant object), m=f_o/f_e . m=140/5.0=28 . Option 3. 1
- If the monochromatic source in Young's double slit experiment is replaced by white light, then Answer: 4. there will be a central bright white fringe surrounded by a few coloured fringes. Key idea: Each colour makes its own fringe patt... 1
- An unpolarised light beam strikes a glass surface at Brewster's angle. Then Answer: 1. the reflected light will be completely polarised but the refracted light will be partially polarised. Key idea: At Brewster's ang... 1
- A light ray enters through a right angled prism at point P with the angle of incidence 30^° as shown in figure. It travels through the prism parallel to its base BC and emerges along the face AC. The refractive index of the prism is: Answer: 3. sqrt5/2 Key idea: The ray leaves along face AC, so its angle of incidence on AC is the critical angle C , with sin C=frac1μ . Let... 1
- Two thin lenses are of same focal lengths (f), but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be : Answer: 1. Infinite For lenses in contact, 1/F=dfrac1f₁+dfrac1f₂ . f₁=+f , f₂=-f : 1/F=1/f-1/f=0 , so F=∞ . The combination behaves like a p... 1
- In the figure shown here, what is the equivalent focal length of the combination of lenses (Assume that all layers are thin)? Answer: 4. -100 cm Add the powers of the two refracting surfaces of the lens ( n=1.5 ) placed in a medium of index 1.6 , using P=n₂-n₁/R . S... 1
- For Young's double slit experiment, two statements are given below:Statement I : If screen is moved away from the plane of slits, angular separation of the fringes remains constant.Statement II : If the monochromatic source is replaced by another mon… Answer: 4. Statement I is true but Statement II is false. Fringe width β=λ D/d , so angular separation θ=β/D=λ/d . Statement I: θ does not d... 1
- Light travels a distance x in time t_1 in air and 10x in time t_2 in another denser medium. What is the critical angle for this medium? Answer: 1. sin⁻¹(10t₁/t₂) Refractive index n=c/v , and the critical angle satisfies sin C=1/n=v/c . Speed in air: c=x/t₁ . Speed in the medi... 1
- Two transparent media A and B are separated by a plane boundary. The speed of light in those media are 1.5 × 10^8 m/s and 2.0 × 10^8 m/s, respectively. The critical angle for a ray of light for these two media is : Answer: 3. sin⁻¹(0.750) Refractive index n=c/v : n_A=3×10⁸/1.5×10⁸=2 and n_B=3×10⁸/2×10⁸=1.5 . Total internal reflection is possible when li... 1
- In a Young's double slit experiment, a student observes 8 fringes in a certain segment of screen when a monochromatic light of 600 nm wavelength is used. If the wavelength of light is changed to 400 nm, then the number of fringes he would observe in… Answer: 1. 12 Fringe width is β=λ D/d . For a fixed region of the screen, the number of fringes is N∝ 1/β∝ 1/λ . N₂=N₁λ₁/λ₂=8×600/400=12 Opt... 1
- A light ray falls on a glass surface of refractive index √(3), at an angle 60°. The angle between the refracted and reflected rays would be : Answer: 4. 90° Use Snell's law: sin60^°=sqrt3sin r⇒sin r=1/2⇒ r=30^° . The reflected ray makes 60^° with the normal, the refracted ray 30^°... 1
- A biconvex lens has radii of curvature, 20 cm each. If the refractive index of the material of the lens is 1.5, the power of the lens is : Answer: 4. +5D Use the lens maker's formula: 1/f=(μ-1)(dfrac1R₁-dfrac1R₂) . For a biconvex lens R₁=+20 cm, R₂=-20 cm: 1/f=0.5(dfrac120+dfrac... 1
- A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of… Answer: 4. 20 cm from the plane mirror, it would be a virtual image. Key idea: lens, then mirror, then lens again. Lens: u=-60,\ f=30⇒ v=60... 1
- A convex lens 'A' of focal length 20 cm and a concave lens 'B' of focal length 5 cm are kept along the same axis with a distance 'd' between them. If a parallel beam of light falling on 'A' leaves 'B' as a parallel beam, then the distance 'd' in cm w… Answer: 2. 15 Key idea: a parallel beam stays parallel only if the lens separation makes the focal points coincide. The convex lens A focuse... 1
- A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since : Answer: 4. all of the above. Key idea: for a telescope objective, large focal length gives larger magnification, and large aperture helps th... 1
- Find the value of the angle of emergence from the prism. Refractive index of the glass is √(3). Answer: 1. 60^° Key idea: a ray hitting a face along its normal goes straight in; then apply Snell's law at the next face. The ray enters th... 1
- In Young's double slit experiment, if the separation between coherent sources is halved and the distance of the screen from the coherent sources is doubled, then the fringe width becomes : Answer: 3. four times Fringe width β=λ D/d . With d→ d/2 and D→2D : β'=λ(2D)/d/2=4β The fringe width becomes four times. Answer: option 3. 1
- Assume that light of wavelength 600 nm is coming from a star. The limit of resolution of telescope whose objective has a diameter of 2 m is : Answer: 1. 3.66×10⁻⁷ rad Limit of resolution of a telescope: Δθ=1.22λ/D . Δθ=frac1.22×600×10⁻⁹2=3.66×10⁻⁷\ rad Answer: option 1. 1
- The Brewsters angle i_b for an interface should be : Answer: 3. 45^° < i_b < 90^° Brewster's law: tan i_b=μ , where μ is the relative refractive index of the interface. Since μ>1 for an ordinar... 1
- A ray is incident at an angle of incidence i on one surface of a small angle prism (with angle of prism A) and emerges normally from the opposite surface. If the refractive index of the material of the prism is μ, then the angle of incidence is nearl… Answer: 3. μ A For a small-angle prism, with emergent ray normal to the second face, the angle of refraction at the second face is 0. Since... 1