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NEET PHYSICSRAY OPTICS AND OPTICAL INSTRUMENTSMedium

Question

A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of a focal length of 10 cm10 \text{ cm}. The diameter of the sun is 1.39×109 m1.39 \times 10^9 \text{ m} and its mean distance from the earth is 1.5×1011 m1.5 \times 10^{11} \text{ m}. What is the diameter of the sun's image on the paper?

A

9.2×10−4 m9.2 \times 10^{-4} \text{ m}

B

6.5×10−4 m6.5 \times 10^{-4} \text{ m}

C

6.5×10−5 m6.5 \times 10^{-5} \text{ m}

D

12.4×10−4 m12.4 \times 10^{-4} \text{ m}

Step-by-Step Solution

  1. Image Formation: Since the sun is at a very large distance (u≈∞u \approx \infty) compared to the focal length of the lens, the rays from the sun are effectively parallel. These rays converge at the focal plane of the lens. Thus, the image distance vv is equal to the focal length ff. v=f=10 cm=0.1 mv = f = 10 \text{ cm} = 0.1 \text{ m}
  2. Magnification Formula: The magnification mm produced by a lens is the ratio of the image size (hih_i) to the object size (hoh_o), which is also equal to the ratio of the image distance (vv) to the object distance (uu). m=hiho=vum = \frac{h_i}{h_o} = \frac{v}{u}
  3. Calculation: Substituting the given values:
  • Object size (Diameter of Sun), ho=1.39×109 mh_o = 1.39 \times 10^9 \text{ m}
  • Object distance (Distance of Sun), u=1.5×1011 mu = 1.5 \times 10^{11} \text{ m}
  • Image distance, v=0.1 mv = 0.1 \text{ m} hi=ho×vuh_i = h_o \times \frac{v}{u} hi=(1.39×109)×0.11.5×1011h_i = (1.39 \times 10^9) \times \frac{0.1}{1.5 \times 10^{11}} hi=1.39×1081.5×1011=1.391.5×10−3 mh_i = \frac{1.39 \times 10^8}{1.5 \times 10^{11}} = \frac{1.39}{1.5} \times 10^{-3} \text{ m} hi≈0.9266×10−3 m=9.27×10−4 mh_i \approx 0.9266 \times 10^{-3} \text{ m} = 9.27 \times 10^{-4} \text{ m}
  1. Conclusion: The calculated diameter is approximately 9.2×10−4 m9.2 \times 10^{-4} \text{ m}.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from RAY OPTICS AND OPTICAL INSTRUMENTS. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSRAY OPTICS AND OPTICAL INSTRUMENTStryingfocusingsunlightequiconvexlength

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