Optics
- Two similar thin equi-convex lenses, of focal length f each, are kept coaxially in contact with each other such that the focal length of the combination is F_1. When the space between the two lenses is filled with glycerin (which has the same refract… Answer: 2. 1 : 2 Two thin lenses in contact: dfrac1F₁=1/f+1/f , so F₁=f/2 . When the gap is filled with glycerin of the same index as glass,... 1
- Pick the wrong answer in the context with rainbow. Answer: 3. An observer can see a rainbow when his front is towards the sun. We pick the wrong statement. Two internal reflections give the s... 1
- In total internal reflection when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be angle of refraction ? Answer: 4. 90^° At the critical angle C , Snell's law gives μ₁sin C=μ₂sin r with sin C=μ₂/μ₁ . So sin r=1 and r=90^° : the refracted ray gra... 1
- In a double slit experiment, when light of wavelength 400 nm was used, the angular width of the first minima formed on a screen placed 1 m away, was found to be 0.2^°. What will be the angular width of the first minima, if the entire experimental app… Answer: 2. 0.15^° For the first minimum, sinθ=λ/d . The angle is small, so θ∝λ . In water, λ'=λ/μ=3/4λ . θ'=3/4×0.2^°=0.15^° . 1
- In Young's double slit experiment the separation d between the slits is 2 mm, the wavelength λ of the light used is 5896 Å and distance D between the screen and slits is 100 cm. It is found that the angular width of the fringes is 0.20^°. To increase… Answer: 3. 1.9 mm Angular fringe width is θ=λ/d , so θ∝1/d for fixed λ . d₂/d₁=θ₁/θ₂⇒ d₂=2×0.20/0.21≈1.9\ mm The slit separation must be dec... 1
- An astronomical refracting telescope will have large angular magnification and high angular resolution, when it has an objective lens of Answer: 2. large focal length and large diameter Angular magnification of an astronomical telescope is m=f_o/f_e , so a large objective foca... 1
- Unpolarised light is incident from air on a plane surface of a material of refractive index 'μ'. At a particular angle of incidence 'i', it is found that the reflected and refracted rays are perpendicular to each other. Which of the following options… Answer: 3. Reflected light is polarised with its electric vector perpendicular to the plane of incidence When reflected and refracted rays a... 1
- An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be Answer: 3. 36 cm away from the mirror Use the mirror formula 1/v+1/u=1/f with f=-15 cm. Case 1: u=-40 : 1/v=-dfrac115+dfrac140=-5/120⇒ v=-24... 1
- The refractive index of the material of a prism is 2 and the angle of the prism is 30^°. One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face… Answer: 3. 45^° The ray retraces its path only if it strikes the silvered face normally. The prism angle is A=30^° . For a ray hitting the s... 1
- The ratio of resolving powers of an optical microscope for two wavelengths λ_1 = 4000 and λ_2 = 6000 is : Answer: 2. 3 : 2 Key idea: resolving power of a microscope is ∝dfrac1λ . R₁/R₂=λ₂/λ₁=6000/4000=3/2 , i.e. 3 : 2. 1
- Two Polaroids P_1 and P_2 are placed with their axis perpendicular to each other. Unpolarised light I_0 is incident on P_1. A third polaroid P_3 is kept in between P_1 and P_2 such that its axis makes an angle 45^° with that of P_1. The intensity of… Answer: 2. I₀/8 Key idea: the first polaroid halves unpolarised light; then use Malus's law I=Icos²θ . After P₁ : I₀/2 . After P₃ (45 ^° ):... 1
- A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle θ,… Answer: 4. y/2x Key idea: when a mirror rotates by θ , the reflected ray turns by 2θ . The spot moves by y=xtan2θ≈2θ x for small angles. So... 1
- A thin prism having refracting angle 10^° is made of glass of refractive index 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of seco… Answer: 1. 6 ^° Key idea: dispersion without deviation means the net deviation is zero: (μ₁-1)A₁=(μ₂-1)A₂ . (1.42-1)×10=(1.7-1)A₂⇒ 4.2=0.7A₂... 1
- Young's double slit experiment is first performed in air and then in a medium other than air. It is found that 8^th bright fringe in the medium lies where 5^th dark fringe lies in air. The refractive index of the medium is nearly : Answer: 3. 1.78 Key idea: compare fringe positions using bright fringe y_n=nλ D/d and dark fringe y_n=(2n-1)λ D/2d . In air, 5th dark fringe... 1
- A linear aperture whose width is 0.02 cm is placed immediately in front of a lens of focal length 60 cm. The aperture is illuminated normally by a parallel beam of wavelength 5×10^-5 cm. The distance of the first dark band of the diffraction pattern… Answer: 3. 0.15 cm For the first dark band in single-slit diffraction, asinθ=λ . sinθ=dfrac5×10⁻⁵0.02=2.5×10⁻³ , a small angle. Distance on... 1
- The interference pattern is obtained with two coherent light sources of intensity ratio n. In the interference pattern, the ratio I_max-I_minI_max+I_min will be Answer: 1. 2sqrt n/n+1 With intensities I₁:I₂=n (take I₁=nI₂ ), I_max=(√(I₁)+√(I₂))² and I_min=(√(I₁)-√(I₂))² . fracI_max-I_minI_max+I_min=4... 1
- A person can see clearly objects only when they lie between 50 cm and 400 cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use, will be Answer: 1. concave, -0.25 diopter The person's far point is 400 cm; to see infinity the lens must form the image of a distant object at 400... 1
- Two identical glass (μ_g=3/2) equiconvex lenses of focal length f each are kept in contact. The space between the two lenses is filled with water (μ_w=4/3). The focal length of the combination is Answer: 3. 3f/4 First find the radius of each lens, then the water lens, then combine powers. Glass lens: 1/f=(3/2-1)(2/R)=1/R , so R=f . Wa... 1
- An air bubble in a glass slab with refractive index 1.5 (near normal incidence) is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness (in cm) of the slab is Answer: 2. 12 Apparent depth =real depth/μ . The bubble is at a fixed real depth x from one face and t-x from the other. x/1.5=5⇒ x=7.5 cm;... 1
- Match the corresponding entries of column 1 with column 2. [Where m is the magnification produced by the mirror]Column 1: (A) m = -2; (B) m = -1/2; (C) m = +2; (D) m = +1/2Column 2: (a) Convex mirror; (b) Concave mirror; (c) Real image; (d) Virtual i… Answer: 1. A → b and c; B → b and c; C → b and d; D → a and d Key idea: real images have negative m (inverted); virtual images have positive... 1
- A astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance : Answer: 4. 54.0 cm Key idea: the objective forms an image of the nearby object; the eyepiece must focus on that image (final image at infini... 1
- In a diffraction pattern due to a single slit of width 'a', the first minimum is observed at an angle 30^° when light of wavelength 5000 Å is incident on the slit. The first secondary maximum is observed at an angle of : Answer: 4. sin⁻¹(3/4) Key idea: single-slit minima satisfy asinθ=nλ ; secondary maxima are approximately at asinθ=(n+1/2)λ . First minimum a... 1
- The intensity at the maximum in a Young's double slit experiment is I_0. Distance between two slits is d = 5λ, where λ is the wavelength of light used in the experiment. What will be the intensity in front of one of the slits on the screen placed at… Answer: 4. I₀/2 Key idea: find the phase difference at the point in front of one slit, then use I=I₀cos²(φ/2) . The point is d/2 from the ce... 1
- The angle of incidence for a ray of light at a refracting surface of a prism is 45^°. The angle of prism is 60^°. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism… Answer: 2. 30^°;\ √(2) Key idea: at minimum deviation the ray passes symmetrically, so r₁=r₂=A/2 and i=A+δ_m/2 . r=30^° ; μ=sin45^°/sin30^°=... 1