Physics - Geometrical Optics Question with Solution | TestHub

Solution:

Let the incident beam be parallel to the x-axis.

1. First reflection (M₁): The beam reflects at an angle $\theta$ with the normal. The reflected ray makes an angle $2\theta$ with the incident direction.

2. Second reflection (M₂): The ray hits the concave mirror M₂. Since the incident ray passes through the focus, it reflects parallel to the principal axis.

3. Third reflection (M₁): The ray reflects off M₁ again. The final image is formed at a distance $f$ from M₂.

The final image coordinates are $x=d-f$ and $y=-f\theta$.

The incident ray is parallel to the x-axis, so its initial y-coordinate is $0$.

After the first reflection from M₁, the ray makes an angle $2\theta$ with the x-axis.

The concave mirror M₂ is placed at $x=d$.

The focal length of M₂ is $f$.

The incident ray on M₂ is parallel to the principal axis (x-axis) after the second reflection.

The final image is formed at a distance $f$ from M₂.

The x-coordinate of the image is $d-f$.

The y-coordinate of the image is $-f\theta$ (due to the small angle approximation and the reflection from M₁).

The final answer is $\boxed{D}$.