JEE Advanced Questions: Optics

Important Question of Optics for JEE Advanced Level Exam:

Q1. The eyepiece and objective of a microscope, of focal lengths 0.3 m and 0.4 m respectively, are separated by a distance of 1.2 m. The eyepiece and the objective are to be interchanged such that angular magnification of the instrument remains same in normal adjustment. What is the new separation between the lenses?

Ans: 1.6 m

 

Q2. A lady cannot see objects closer than 40 cm from the left eye and closer than 100 cm from the right eye. While on a mountaineering trip, she is lost from her team. She tries to make an astronomical telescope from her reading glasses to look for her teammates. (a) Which glass should she use as the eyepiece ? (b) What magnification can she get with relaxed eye ?

Ans: right lens, 2

 

Q3. Find the maximum magnifying power of a compound microscope having a 25 diopter lens as the objective, a 5 diopter lens as the eyepiece and the separation 30 cm between the two lenses. the least distance for clear vision is 25 cm.

Ans: 67/8

Q4. A compound microscope consists of an objective of focal length 1.0 cm and an eyepiece of focal , length 5.0 cm separated by 12.2 cm (a) At what distance from the objective should an object be placed to focus it properly so that the final image is formed at the least distance of clear vision (25 cm) ? (b) Calculate the angular magnification in this case.

Ans: (a) – 241/211 cm , (b) 42.2

 

Q5. (a) A thin glass plate of thickness t and refractive index μ is inserted between screen & one of the slits in a Young’s experiment. If the intensity at the centre of the screen is I, what was the intensity at the same point prior to the introduction of the sheet. (b) One slit of a Young’s experiment is covered by a glass plate (μ1 = 1.4) and the other by another glass plate (μ2 = 1.7) of the same thickness. The point of central maxima on the screen, before the plates were introduced is now occupied by the third bright fringe. Find the thickness of the plates, the wavelength of light used is 4000 Å.

Ans: (b) 4μm

Q6. In a YDSE experiment, the distance between the slits & the screen is 100 cm . For a certain distance between the slits, an interference pattern is observed on the screen with the fringe width 0.25 mm. When the distance between the slits is increased by Δd = 1.2 mm, the fringe width decreased to n = 2/3 of the original value. In the final position, a thin glass plate of refractive index 1.5 is kept in front of one of the slits & the shift of central maximum is observed to be 20 fringe width. Find the thickness of the plate & wavelength of the incident light.

Q7.A plastic film with index of refraction 1.80 is put on the surface of a car window to increase the reflectivity and thereby to keep the interior of the car cooler. The window glass has index of refraction 1.60. (a) What minimum thickness is required if light of wavelength 600 nm in air reflected from the two sides of the film is to interfere constructively? (b) It is found to be difficult in manufacture and install coatings as thin as calculated in part (a) What is the next greatest thickness for which there will also be constructive interference?

Ans: Q.11 (a) 8.33 × 10^–8 m, (b) 2.5 × 10^–7 m

Q8. The Young’s double slit experiment is done in a medium of refractive index 4/3. A light of 600 nm wavelength is falling on the slits having 0.45 mm separation. The lower slit S2 is covered by a thin glass sheet of thickness 10.4μm and refractive index 1.5. The interference pattern is observed on a screen placed 1.5 m from the slits as shown [JEE’99]

(a) Find the location of the central maximum (bright fringe with zero path difference) on the y-axis.

(b) Find the light intensity at point O relative to the maximum fringe intensity.

(c) Now, if 600 nm light is replaced by white light of range 400 to 700 nm, find the wavelengths of the light that form maxima exactly at point O . [All wavelengths in this problem are for the given medium of refractive index 4/3. Ignore dispersion

Ans: (a) y = – 13/3 mm, (b) intensity at O = 0.75I max (c) 650 nm, 433.33 nm

Q9. Two coherent light sources A and B with separation 2λ are placed on the x-axis symmetrically about the origin. They emit light of wavelength λ. Obtain the positions of maxima on a circle of large radius lying in the xy-plane and with centre at the origin.

Q10. In a Young’s double slit experiment, two wavelengths of 500 nm and 700 nm were used. What is the minimum distance from the central maximum where their maximas coincide again? Take D/d = 103 . Symbols have their usual meanings.

Ans: 3.5 mm

Q11. Two symmetric double-convex lenses L1 & L2 with their radii of curvature 0.2 m each are made from glasses with refractive index 1.2 & 1.6 respectively. The lenses with a separation of 0.345 m are submerged in a transparent liquid medium with a refractive index of 1.4. Find the focal lengths of lens L1 & L2 . An object is placed at a distance of 1.3 m from L1 , find the location of its image while the whole system remains inside the liquid.

Ans: f 1 = − 70 cm, f2 = 70 cm, V = 560 cm to the right of L2

Q12. A meniscus lens is made of a material of refractive index µ2 . Both its surfaces have radii of curvature R. It has two different media of refractive indices µ1 and µ3 respectively, on its two sides (shown in the figure). Calculate its focal length for µ1 < µ2 < µ3 , when light is incident on it as shown 

 

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