Questions OBJECTIVE - I and Answer (Geometrical Optics) HC Verma Part 1 (1-9)

 Q#1

A point source of light is placed in front of a plane mirror.
(a) All the reflected rays meet at a point when produced backward.
(b) Only the reflected rays close to the normal meet at a point when produced backward.
(c) Only the reflected rays making a small angle with the mirror, meet at a point when produced backward.
(d) Light of different colors makes different images.

Answer: (a)
See the diagram below,
Take any ray PR which is reflected at Q and QR is the reflected ray. Since the angle of incidence is equal to the angle of reflection,

∠PQN = ∠RQN = ∠OPQ = α

RQ, when produced back, meets PO produced at P'.
In right-angled triangles PQO and P'QO,

∠QPO = ∠QP'O = α

Thus both are equal in all respect.
So, PO = P'O.
For any other ray, it can be proved.
Hence the option (a).
P' becomes a virtual image of P.

Q#2
Total internal reflection can take place only if
(a) Light goes from optically rarer medium (smaller refractive index) to optically denser medium.
(b) light goes from optically denser medium to rarer medium
(c) the refractive indices of the two media are close to each other
(d) the refractive indices of the two media are widely different.

Answer: (b)
When the light goes from a denser medium to lighter medium, it goes away from the normal. When the angle of incidence is increased, the angle of refraction becomes 90°. It is the critical angle. Now if the angle is increased further, the phenomenon of refraction is changed to total internal reflection.

Q#3
In image formation from spherical mirrors, only paraxial rays are considered because they are
(a) easy to handle geometrically
(b) contain most of the intensity of the incident light
(c) form nearly a point image of a point source
(d) show a minimum dispersion effect.

Answer: (c)
The reflected rays from a point source in a spherical mirror do not meet at a single point. To avoid it, rays close to the principal axis (Paraxial rays) are taken. It forms nearly a point image of a point source.

Q#4
A point object is placed at a distance of 30 cm from a convex mirror of focal length 30 cm. The image will form at
(a) infinity
(b) pole
(c) focus
(d) 15 cm behind the mirror.

Answer: (d)
The option can be selected by suitable reasoning. In a convex mirror, the object at infinity has its image at the focus behind the mirror.
So, option (c) is not correct because the object here is not at infinity.

The image in a convex mirror never forms at infinity. The option (a) is not correct.
The image will be near the pole if the object is near the pole, which is not the case here. The option (b) is not correct.

The only option left is (d) and the image position is between focal length and the pole for the object between infinity and the pole. Hence the option (d) is correct.

Q#5
Figure (19-Q2) shows two rays A and B being reflected by a mirror and going as A' and B'. The mirror
(a) is plane
(b) is convex
(c) is concave
(d) may be any spherical mirror.

Answer: (a)
The parallel rays after reflection are still parallel, which is possible only in a plane mirror. Concave or convex mirrors either converge or diverge the parallel rays. Hence the option (a) is correct.

Q#6
The image formed by a concave mirror
(a) is always real
(b) is always virtual
(c) is certainly real if the object is virtual
(d) is certainly virtual if the object is real.

Answer: (c)
The image formed by a concave mirror may be real or virtual depending upon the position of the object. Hence the option (a) and (b) are wrong. Only the real object placed between the focus and the pole has a virtual image otherwise it is real. The option (d) is not correct. Hence the only option remaining is (c).

Q#7
Figure (18-Q3) shows three transparent media of refractive indices µ₁, µ₂, and µ₃. A point object O is placed in the medium µ₂. If the entire medium on the right of the spherical surface has a refractive index µ₁, the image forms at O'. If this entire medium has refractive index µ₃, the image forms at O". In the situation shown,
(a) the image forms between O' and O".
(b) the image forms to the left of O'.
(c) the image forms to the right of O".
(d) two images form, one at O' and the other at O".

Answer: (d)
The rays incident on the surface above the principal axis will be refracted in the medium of RIµ₃ and form the image at O". But the rays falling below the axis will be refracted in the medium having RIµ₁ and the image will be formed at O'. Hence two images will be formed.

Q#8
Four modifications are suggested in the lens formula to include the effect of the thickness t of the lens. Which one is likely to be correct?
(a) 1/v – 1/u = t/uf
(b) t/v² – 1/u = 1/f
(c) 1/(v – t) – 1/(u + t) = 1/f
(d) 1/v – 1/u + t/uv = t/f

Answer: (c)
The thickness of the lens will affect the object distance or image distance. Either the thickness t will be added or subtracted to u or v. It will not be in a proportion as shown in the options (a), (b) and (d). Hence the option (c) is correct.

Q#9
A double convex lens has two surfaces of equal radii R and refractive index µ = 1.5, we have,
(a) f = R/2
(b) f = R
(c) f = –R
(d) f = 2R

Answer: (b)
From lens makers formula

1/f = (µ – 1){1/R – 1/R'}
here µ = 1.5, R' = –R
1/f = (0.5 x 2)/R = 1/R
f = R

Hence the option (b) is true.  

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