Question

To find the focal length of a convex mirror, a student records the following data : The focal length of the convex lens is $f_1$ and that of mirror is $f_2$. Then taking index correction to be negligibly small, $f_1$ and $f_2$ are close to :

• A. $f_1=12.7 \, cm$ $ f_2 = 7.8 \, cm$
• B. $f_1= 7.8 \, cm$ $ f_2 = 12.7 \, cm$
• C. $f_1= 7.08 \, cm$ $ f_2 = 25.4 \, cm$
• D. $f_1= 15.6 \, cm$ $ f_2 = 25.4 \, cm$

Answer 1

The Correct Option is B

To find the focal lengths of a convex mirror and a convex lens, a student conducts an experiment. The focal length of a convex mirror is typically measured using an auxiliary convex lens and a known method such as the "Lens-Mirror" experiment. Here, the basic concept revolves around forming an image using both the lens and the mirror and applying the mirror formula.

The focal length of a convex mirror, f_2, can be indirectly measured by using a convex lens with a known focal length f_1. The setup generally consists of:

1. Positioning an illuminated object in front of both the mirror and lens.
2. Finding the position of the real image formed by the lens.
3. Utilizing the focal length of the lens, f_1, to calculate the combined focal length of the system, and thereby determining f_2.

Given the question, we have several options for the values of f_1 and f_2. By understanding the relationship between focal lengths and the method typically used, the experiments commonly result in:

For a compact lens-mirror system:

• The focal length of a convex lens is generally shorter than that of a convex mirror in typical setups where f_1 helps in measuring the larger radius of curvature advantageously facilitated by f_2.

Among the given options:

• Option 1: f_1 = 12.7 \, \text{cm}, f_2 = 7.8 \, \text{cm} — This seems incorrect because f_2 should generally be larger than f_1 for practical setups.
• Option 2: f_1 = 7.8 \, \text{cm}, f_2 = 12.7 \, \text{cm} — This is the correct answer based on expected experimental results where f_2 is longer.
• Option 3: f_1 = 7.08 \, \text{cm}, f_2 = 25.4 \, \text{cm} — Makes f_2 significantly larger which is less typical.
• Option 4: f_1 = 15.6 \, \text{cm}, f_2 = 25.4 \, \text{cm} — Both values exceed expected ranges for practicality and usability.

Hence, the correct answer is Option 2: f_1 = 7.8 \, \text{cm}, f_2 = 12.7 \, \text{cm}.