NEET 2025 Physics Lens Systems MCQ Question

To determine the power and magnification of a combination of four similar thin convex lenses arranged axially in contact, we apply the fundamental principles of optics for lens systems. Let's break down the problem step by step.

1. Equivalent Power of the Lens Combination

When multiple thin lenses are placed in contact, the equivalent power $P_{eq}$ can be computed by summing the individual powers of each lens. The formula for the equivalent power of $n$ lenses in contact is:

$$P_{eq} = P_1 + P_2 + P_3 + ... + P_n$$

Given that all four lenses have the same power $p$:

$$P_{eq} = p + p + p + p = 4p$$

This means the total power of the combination is $4p$.

2. Total Magnification of the Lens Combination

The total magnification $M_{total}$ of a system of lenses is the product of the magnifications of the individual lenses. For $n$ lenses, the total magnification is given by:

$$M_{total} = M_1 \cdot M_2 \cdot M_3 \cdot ... \cdot M_n$$

Since each lens has the same magnification $m$:

$$M_{total} = m \cdot m \cdot m \cdot m = m^4$$

This indicates that the total magnification of the combination is $m^4$.

Summary of Results

Thus, for four similar thin convex lenses arranged in contact:

• The equivalent power of the combination is $4p$.
• The total magnification of the combination is $m^4$.

Correct Answer

Therefore, the correct answer to the question is:

D) $4p$ and $m^4$.

3. Explanation of Incorrect Options

Now, let's analyze the other options provided in the question:

• Option B: $p^4$ and $4m$

  • Incorrect because the power is incorrectly expressed as $p^4$. The correct calculation shows that the power is $4p$, not $p^4$. The magnification $4m$ is also incorrect; it should be $m^4$.

• Option C: $4p$ and $m^4$

  • This option is partially correct regarding the power, but it does not match the correct analysis since we confirmed that the magnification is $m^4$.

• Option D: $p^4$ and $m^4$

  • Incorrect because the power is again incorrectly stated as $p^4$. The correct total power is $4p$, while the magnification $m^4$ is indeed correct.

Conclusion

In conclusion, the correct answer is option A: $4p$ for power and $m^4$ for magnification, following the defined rules for combining optical components in a lens system.