## Tuesday, June 09, 2015

### KEAM 2015 Engineering Questions on Optics

“Man perfected by society is the best of all animals; he is the most terrible of all when he lives without law and without justice.”
Aristotle

Let us discuss the questions (MCQ) on optics which appeared in KEAM Engineering 2015 question paper. Here are the questions:

(1) A ray of light is incident normally on one refracting surface of an equilateral prism. If the refractive index of the material of the prism is 1.5, then

(a) the emergent ray is deviated by 30º

(b) the emergent ray is deviated by 60º

(c) the emergent ray just grazes the second refracting surface

(d) the ray undergoes total internal reflection at the second refracting surface

(e) the ray emerges normally from the second refracting surface
The correct option is (d) as explained below:

The ray PQ incident normally on the face AB of the prism proceeds undeviated through the prism and strikes the face AC at the point R, as shown in the adjoining figure. From the right angled triangle AQR it is clear that angle QRA = 30º. Therefore, it follows that the angle of incidence QRN at the face AC is 60º. Since this is greater than the critical angle (which is slightly less than 42º for the material of refractive index 1.5), the ray is totally reflected along RS as shown in the figure.
[You may calculate the critical angle using the equation,
n = 1/sinC where n is the refractive index and C is the critical angle.
Therefore sinC = 1/1.5 = 0.66667 and C = sin–1(0.66667) = 41.8º]
(2) An aperture of size a is illuminated by a parallel beam of light of wave length λ. The distance at which ray optics has a good approximation is
(a) a2
(b) λ/a2
(c) λ/a
(d) λ2/a
(e) ) a2λ
The angular width of the central maximum in the diffraction pattern produced by an aperture of size a illuminated by a parallel beam of light of wave length λ is λ/a. In traveling a distance z the diffracted beam acquires a width zλ/a. The distance beyond which the spreading of the beam becomes significant compared to the with a of the slit can be obtained by equating the width of the beam to the width of the slit. Thus we have
through a prism the beam continues to be parallel and hence the wave front continues to be plane. The correct option is (c).   zλ/a = a from which z = a2.
This distance z can be taken as the distance at which ray optics has a good approximation. So the correct option is (a).
(3) Two plane wave fronts of light are incident on a thin convex lens and on the refracting face of a thin prism. After refraction at them the emergent wave fronts respectively become
(a) plane wave front and plane wave front
(b) plane wave front and spherical wave front
(c) spherical wave front and plane wave front
(d) spherical wave front and spherical wave front
(e) elliptical wave front and spherical wave front

A plane wave front is made by a beam of parallel rays. On passing through a convex lens, the beam becomes convergent and hence the wave front becomes spherical. On passing through a prism the beam continues to be parallel and hence the wave front continues to be plane. The correct option is (c).
(4) If a ray of light is incident at a glass surface at the Brewster's angle of 60º, then the angle of deviation inside glass is
(a) 90º
(b) 60º
(c) 45º
(d) 30º
(e) 15º
When the ray of light is incident on the glass surface at Brewster’s angle, the refracted ray is at right angles to the reflected ray (Fig.). Since the angle of reflection is equal to the angle of incidence, the angle between the reflected ray and the glass surface is 30º. Therefore, the angle between the refracted ray and the glass surface is 60º. The angle of deviation inside glass is evidently 30º as given in option (d).
(5) Identify the wrong sign convention
(a) The magnification for virtual image formed by a convex lens is positive
(b) The magnification for real image formed by a convex lens is negative
(c) The height measured normal to the principal axis upwards is positive
(d) The distances measured in the direction of incident light is positive
(e) The magnification for virtual image formed by a concave lens is negative
Even though the image of a real object formed by a concave lens is virtual, the height of the object and the virtual image are to be measured along the same direction since the virtual image is erect. The magnification for virtual image formed by a concave lens is therefore positive. Therefore the wrong sign convention is given in option (e).