A Converging bundle of light rays in the shape of

To solve this problem, we need to analyze the situation involving the lens and the light rays. The lens has a power of 5 diopters (D), which can be converted to focal length using the formula:

Understanding Lens Power

The relationship between power (P) and focal length (f) is given by:

P = 1/f

Thus, the focal length of the lens is:

f = 1/P = 1/5 = 0.2 m = 20 cm

Analyzing the Light Rays

The original cone of light has a vertex angle of 45°. When it passes through the lens, it converges to a point. The new cone of light has a vertex angle of 0°, meaning the rays are parallel after passing through the lens.

Calculating the Tangent of the Angle

For a cone with a vertex angle of 45°, the tangent of half the angle is:

tan(22.5°) = 1

However, since the new cone has a vertex angle of 0°, we need to find the tangent of the angle that corresponds to the new configuration.

Finding the Correct Option

Given that the light rays are parallel after passing through the lens, we can deduce that:

• If the rays converge to a point, the tangent of the angle formed by the rays can be calculated based on the geometry of the setup.
• Since the rays are parallel, the tangent of the angle is effectively the ratio of the opposite side to the adjacent side in the triangle formed.

In this case, the correct answer for tan(θ) when the vertex angle is 0° is:

tan(θ) = 2

Final Answer

The answer is (B) 2.