AIIMS 2006 Physics Lenses MCQ Question

To solve the problem of determining the magnification produced by a magnifying converging lens, we will use the lens formula and the magnification formula. Let's break down the problem step by step.

Given Information:

• Focal length of the lens, $f = 10 \, \text{cm}$
• Object distance (the distance of the wire mesh from the lens), $u = -8 \, \text{cm}$ (the negative sign indicates that the object is on the same side as the incoming light)

Step 1: Calculate the Image Distance

We can use the lens formula, which is given by:

$$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$

Where:

• $f$ is the focal length,
• $v$ is the image distance,
• $u$ is the object distance.

Rearranging the formula to solve for $v$:

$$\frac{1}{v} = \frac{1}{f} + \frac{1}{u}$$

Substituting the known values:

$$\frac{1}{v} = \frac{1}{10} + \frac{1}{-8}$$

Calculating the right-hand side:

• Convert to a common denominator, which is 40:

$$\frac{1}{10} = \frac{4}{40}, \quad \frac{1}{-8} = -\frac{5}{40}$$

Now, add the fractions:

$$\frac{1}{v} = \frac{4}{40} - \frac{5}{40} = -\frac{1}{40}$$

Taking the reciprocal gives:

$$v = -40 \, \text{cm}$$

Step 2: Calculate the Magnification

The magnification $M$ produced by a lens is given by the formula:

$$M = -\frac{v}{u}$$

Substituting the values of $v$ and $u$:

$$M = -\frac{-40}{-8} = \frac{40}{8} = 5$$

Conclusion:

The magnification produced by the lens is $M = 5$. Therefore, the correct answer is A) 5.

Explanation of Other Options:

• B) 8: This option suggests a higher magnification than what we calculated. If the image distance or object distance were different, it might increase, but with the given values, it's not possible.
• C) 10: Similar reasoning applies; this would require a different configuration of $u$ or $f$.
• D) 20: This option indicates an unrealistic magnification for the given parameters, as it would imply that the object is observed in a significantly enlarged manner, which is not supported by our calculations.

Thus, the only correct answer, supported by the computations, is A) 5.