AIIMS 2007 Physics Camera Lens MCQ Question

To solve this question, we need to understand the relationship between the aperture size, exposure time, and the amount of light that reaches the camera sensor. The aperture is a crucial component in photography, as it determines how much light enters the camera.

Key Concepts

1. Aperture and Exposure: The size of the aperture is expressed in terms of f-stops. When the aperture size increases (i.e., when the f-number decreases), more light enters the camera, which means the exposure time can be reduced to achieve the same level of brightness in the photograph.

2. Exposure Time: Exposure time is the duration for which the camera shutter remains open to allow light to reach the sensor. A shorter exposure time means less light reaches the sensor.

3. Relationship Between Aperture Size and Exposure Time: The relationship can be described by the following formula: $T_1 / T_2 = (A_2 / A_1)^2$ where:

   • $T_1$ is the original exposure time,
   • $T_2$ is the new exposure time,
   • $A_1$ is the original aperture size (in terms of f-number),
   • $A_2$ is the new aperture size.

Given Data

• Original aperture: $f$
• New aperture: $1.4f$
• Original exposure time: $T_1 = \frac{1}{60}$ s

Calculation Steps

1. Calculate the Ratio of Apertures:

   $$\text{Ratio of apertures} = \frac{A_2}{A_1} = \frac{1.4f}{f} = 1.4$$

2. Apply the Exposure Time Formula: Using the formula mentioned above:

   $$\frac{T_1}{T_2} = (1.4)^2 = 1.96$$

   Rearranging gives:

   $$T_2 = \frac{T_1}{1.96}$$

   Plugging in the value for $T_1$:

   $$T_2 = \frac{\frac{1}{60}}{1.96} = \frac{1}{60 \times 1.96} \approx \frac{1}{117.6}$$

3. Convert to a Practical Exposure Time: To find a more standard exposure time, we can round this value. The closest practical exposure time for $T_2$ is found by calculating:

   $$T_2 \approx \frac{1}{118} \text{ s}$$

   This can be estimated to a fraction that is closest to standard shutter speeds. We can check the options provided to see which is nearest to this value.

4. Finding the Closest Option: Evaluating the given options:

   • A) $\frac{1}{42}$ = 0.0238 s
   • B) $\frac{1}{56}$ = 0.0179 s
   • C) $\frac{1}{72}$ = 0.0139 s
   • D) $\frac{1}{31}$ = 0.0323 s

   The correct answer is D, $\frac{1}{31}$, because it is the closest to $\frac{1}{118}$ when considering practical exposure times.

Conclusion

Thus, when the aperture size increases from $f$ to $1.4f$, the exposure time decreases from $\frac{1}{60}$ s to approximately $\frac{1}{31}$ s, making option D the correct answer.

Why Other Options are Incorrect

• Option A: $\frac{1}{42}$ is too long, allowing more light than needed.
• Option B: $\frac{1}{56}$ is also too long, similar reasoning as above.
• Option C: $\frac{1}{72}$ is still not enough reduction in exposure time.

Thus, D is the only option that correctly reflects the necessary adjustment in exposure time when increasing aperture size.