IIT-JEE 2007- Three Questions from Optics

The following three questions appeared in IIT-JEE (Part I) 2007 question paper:

(1) In an experiment to determine the focal length (f) of a concave mirror by the u-v method,a student places the object pin A on the principal axis at a distance x from the pole P. The student looks at the pin and its inverted image from a distance, keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then,

(a) x less than f (b) f less than x less than 2f (c) x = 2f (d) x greater than 2f

This question is a simple one and is intended to check your understanding of techniques used in experimental physics in addition to your theoretical knowledge. Since the image appears to the right of the object when the student shifts his eye towards the left, the image is nearer to the student and hence the image distance ‘v’ is greater than the object distance ‘u’. This is possible only if the object is placed between f and 2f. So the correct option is (b).

[The image is real since it is inverted as mentioned in the question. The problem can be worked out even if this fact is not mentioned in this problem].

(2) A ray of light traveling in water is incident on its surface open to air. The angle of incidence is θ, which is less than the critical angle. Then there will be

(a) only a reflected ray

(b) only a refracted ray and no reflected ray

(c) a reflected ray and a refracted ray and the angle between them would be less

than 180° – 2θ

(d) A reflected ray and a refracted ray and the angle between them would be

greater than 180° –2θ

If the angle of incidence is not equal to or greater than the critical angle, there will be partial transmission and partial reflection. As is evident from the figure, the angle between the reflected ray and the refracted ray (angle SQR) is less than 180° – 2θ. The correct option is (c).

(3) STATEMENT-1

The formula connecting u,v and f for a spherical mirror is valid only for mirrors
whose sizes are very small compared to their radii of curvature

because

STATEMENT-2

Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

(a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct

explanation for Statement-1

(b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct

explanation for Statement-1

(c) Statement-1 is True, Statement-2 is False

(d) Statement-1 is False, Statement-2 is True

This is an assertion-reason type MCQ. You might have noted that the formula connecting u, v and f was derived considering rays close to the principal axis so that only a small portion of the mirror surrounding the pole is involved. Statement-1 is therefore true. Statement-2 is false since the laws of reflection are applied to a ray which is incident at a given point. The size of the mirror and its curvature are not involved here.

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