JEE Physics Ray Optics And Optical Instruments MCQs Set 31

Answer: (a) real, inverted and of the same size

Explanation:
1. The object is at the centre of curvature (2f).
2. The image is at 2f, real, inverted and of the same size.

Teacher's Note:
1. Recall the basic fact.

Answer: (b) lies between 2 and √2

Explanation:
1. μ = sin((A + D)/2)/sin(A/2) = 2 cos(A/2) when D = A.
2. For A between 0 and 90° this lies between 2 and √2.

Teacher's Note:
1. Recall the basic fact.

Answer: (d) perpendicular to the tangent plane at the point of incidence and passes through the centre of curvature

Explanation:
1. The radius drawn to the point of incidence is the normal.

Teacher's Note:
1. Recall the basic fact.

Answer: (d) \( \frac1f=(\mu-1)\left(\frac1{R_1}-\frac1{R_2}\right) \)

Explanation:
1. The lens maker's formula is 1/f = (μ - 1)(1/R1 - 1/R2).

Teacher's Note:
1. Recall the basic fact.

Answer: (a) simple microscope

Explanation:
1. A simple microscope forms an erect virtual image.
2. The compound microscope and the astronomical telescope give inverted images.

Teacher's Note:
1. Recall the basic fact.

Answer: (d) the eye is not able to decrease the focal length beyond a limit

Explanation:
1. The ciliary muscles cannot make the lens thick enough to reduce f below a limit.

Teacher's Note:
1. Recall the basic fact.

Answer: (c) becomes parallel to the base of the prism

Explanation:
1. At minimum deviation the ray inside is parallel to the base.

Teacher's Note:
1. Recall the basic fact.

Answer: (d) \( \frac{\mu t}{c} \)

Explanation:
1. Time = t/v = t μ/c.

Teacher's Note:
1. Recall the basic fact.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. sin θc = 1/μ and violet has the smallest wavelength, so the largest μ and the smallest θc.
2. The reason gives exactly this link.

Teacher's Note:
1. Compare the two statements.

Answer: (a) a vernier scale provided on the microscope

Explanation:
1. The travelling microscope has a vernier scale.

Teacher's Note:
1. Recall the basic fact.

Answer: (b) A-3, B-1, C-2, D-4

Explanation:
1. Mirage is due to total internal reflection (A-3).
2. Apparent depth is due to refraction (B-1).
3. The blue sky is due to scattering (C-2).
4. A rainbow is due to dispersion (D-4).

Teacher's Note:
1. Match the phenomenon to its cause.

Answer: (b) 2 cm

Explanation:
1. The eye-lens to retina distance, about 2 cm, equals the focal length of the relaxed lens.

Teacher's Note:
1. Recall the basic fact.

Answer: (c) 20 cm

Explanation:
1. The silvered lens acts as a concave mirror of focal length R/(2μ) = 30/3 = 10 cm.
2. A real image of equal size forms when the object is at 2f = 20 cm.

Teacher's Note:
1. Recall the basic fact.

Answer: (b) 2 cos A

Explanation:
1. The ray returns along its path, so it hits the silvered face normally and r = A.
2. sin 2A = μ sin A gives μ = 2 cos A.

Teacher's Note:
1. Recall the basic fact.

Answer: (b) 10°

Explanation:
1. No net deviation needs (μ1 - 1)A1 = (μ2 - 1)A2.
2. 0.5 × 15 = 0.75 × A2, so A2 = 10°.

Teacher's Note:
1. Recall the basic fact.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Since ω1 and ω2 are positive, the condition requires f1 and f2 of opposite sign, so one lens must be concave.
2. The reason states the condition.

Teacher's Note:
1. Compare the two statements.

Answer: (c) 50 cm

Explanation:
1. The lens forms the image at v = 60 cm.
2. For the final image to coincide with the object, the rays must retrace their path, so the mirror must be placed such that its centre of curvature lies at that image point.
3. The mirror is therefore 60 - 10 = 50 cm from the lens.

Teacher's Note:
1. Recall the basic fact.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. A plane mirror forms a real image if the object is virtual, so the assertion is true.
2. A real object always gives a virtual image, so the reason is true but it does not explain the assertion.

Teacher's Note:
1. Compare the two statements.

Answer: (c) form nearly a point image of a point source

Explanation:
1. Paraxial rays converge to nearly a single point, avoiding spherical aberration.

Teacher's Note:
1. Recall the basic fact.

Answer: (c) i = 45°, e = 45°

Explanation:
1. i = (A + D)/2 = (60 + 30)/2 = 45° and e = i = 45°.

Teacher's Note:
1. Recall the basic fact.

Answer: (b) secondary rainbow

Explanation:
1. The secondary rainbow involves two internal reflections.

Teacher's Note:
1. Recall the basic fact.

Answer: (a) refraction

Explanation:
1. Atmospheric refraction raises the lower edge more than the upper edge.

Teacher's Note:
1. Recall the basic fact.

Answer: (c) A is true, but R is false.

Explanation:
1. 1/f = 0.5(2/R) = 1/R, so f = R and the assertion is true.
2. The reason (R/2) is false.

Teacher's Note:
1. Compare the two statements.

Answer: (b) 3 : 5

Explanation:
1. The power of the divergent lens is 2 - 5 = -3 D.
2. Achromatism needs ω1 P1 + ω2 P2 = 0, so ω1/ω2 = 3/5.

Teacher's Note:
1. Recall the basic fact.

Answer: (b) 100 cm

Explanation:
1. 1/f = (1.6 - 1)/60 = 0.01, so f = 100 cm.

Teacher's Note:
1. Recall the basic fact.