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RAY OPTICS AND OPTICAL INSTRUMENTS-25 Quiz

Dear Readers,

JEE Advanced Physics Syllabus can be referred by the IIT aspirants to get a detailed list of all topics that are important in cracking the entrance examination. JEE Advanced syllabus for Physics has been designed in such a way that it offers very practical and application-based learning to further make it easier for students to understand every concept or topic by correlating it with day-to-day experiences. In comparison to the other two subjects, the syllabus of JEE Advanced for physics is developed in such a way so as to test the deep understanding and application of concepts.

Q1. Statement 1: Using Huygen’s eye-piece measurements cab be taken but are not correct.
Statement 2: The cross wires, scale and final image are not magnified proportionately because the image of the object is magnified be two lenses, whereas the cross wire scale is magnified by one lens only. Identify the correct one of the following
  •   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is False
  •   Statement 1 is False, Statement 2 is True
Solution
(c) Using Huygen’s eye-piece, measurements can be taken but not accurately due to the reason given.

Q2.Statement 1: The focal length of the mirror is f and distance of the object from the focus is u, the magnification of the mirror is f/u
Statement 2: Magnification =(Size of image)/(Size of object)
  •   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is False
  •   Statement 1 is False, Statement 2 is True
Solution
(a) Magnification produced by mirror m=I/O=f/(f-u)=f/x x is distance from focus

Q3.   Statement 1: Different colours travel with different speed in vacuum
Statement 2: Wavelength of light depends on refractive index of medium
  •   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is False
  •   Statement 1 is False, Statement 2 is True
Solution
The velocity of light of different colours (all wavelengths) is same in vacuum and μ∝1/λ

Q4. Statement 1: The focal length of the refractive of the telescope is larger than that of eye piece Statement 2: The resolving power of telescope increases when the aperture of objective is small
  •   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is False
  •   Statement 1 is False, Statement 2 is True
Solution

(d)
The magnifying power of telescope in relaxed state is m=f_0/f_e
So, for high magnification, the focal length of objective length should be larger than of eye-piece
Resolving power of a telescope =d/(1.22 λ)
For high resolving power. Diameter (d) of objective should be higher

Q5. Statement 1: A beam of white light enters the curved surface of a semicircular piece of glass along the normal. The incoming beam is moved clockwise (so that the angle θ increases), such that the beam always enters along the normal to the curved side. Just before the refracted beam disappears, it becomes predominantly red
Statement 2: The index of refraction for light at the red end of the visible spectrum is more than at the violet end
  •   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is False
  •   Statement 1 is False, Statement 2 is True
Solution
 (c) The index of refraction of light at the red end of the visible spectrum is lesser than at the violet end. Statement II is false

Q6. Statement 1: When a light wave travels from a rarer to a denser medium, it loses speed. The reduction in speed implies a reduction in energy carried by the light wave
Statement 2: The energy of a wave is proportional to wave frequency
  •   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is False
  •   Statement 1 is False, Statement 2 is True
Solution
When a light wave travels from a rarer to a denser medium it loses speed,
but energy carried by the wave does not depend on its speed


Q7.Statement 1: A double convex lens (μ=1.5) has focal length 10 cm. When the lens is immersed in water (μ=4/3) its focal length becomes 40 cm
Statement 2: 1/f=(μ_1-μ_m)/μ_m (1/R_1 -1/R_2 )
  •   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is False
  •   Statement 1 is False, Statement 2 is True
Solution
(a)
Focal length of lens immersed in water is four times the focal length of lens in air. It means
f_ω=4f_a=4×10=40 cm
Q8. Statement 1: A short sighted person cannot see objects clearly when placed beyond 50 cm. He should use a concave lens of power 2 D.
Statement 2: Concave lens should form image of an object at infinity placed at a distance of 50 cm.
  •   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is False
  •   Statement 1 is False, Statement 2 is True
Solution
(b) We know that power of lens is a reciprocal of its focal length, hence P=1/f=1/(50/100)=2D
Since, lens is concave hence, its power will be 2D. If the object is placed at infinity then
μ=∞,v= ?,f=50 cm
From the formula, 1/v-1/u=1/f
1/v-1/∞=1/(-50)
v=-50 cm
Thus, concave lens will form an image of the object at infinity at a distance of 50 cm.


Q9. Statement 1: A concave mirror and convex lens both have the same focal length in air. When they are submerged in water, they will still have the same focal length
Statement 2: The refractive index of water is greater than the refractive index of air
  •   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is False
  •   Statement 1 is False, Statement 2 is True
Solution
(d) If a mirror is placed in a medium other than air its focal length does not change as f=R/2, but for the lens
1/f_a =(_a n^g-1)(1/R_1 -1/R_2 )
and 1/f_w =(_w n^g-1)(1/R_1 -1/R_2 )
As _w n^g less than _a n^g, hence focal length of lens in water increases. The refractive index of water is 4/3 and that of air is 1. Hence, μ_w>μ_a


Q10. Statement 1: All the materials always have the same colour, whether viewed by reflected light or through transmitted light
Statement 2: The colour of material does not depend on nature of light

  •   Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •   Statement 1 is True, Statement 2 is False
  •   Statement 1 is False, Statement 2 is True
Solution

It is not necessary for a material to have same colour in reflected and transmitted light. A material may reflect one colour strongly and transmit some other colour. For example, some lubricating oils reflect green colour and transmit red. Therefore, in reflected light, they will appear green and in transmitted light, they will appear red

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