To solve this problem, we need to analyze the behavior of light when it reflects off both a concave mirror and a plane mirror. The key points to consider are the properties of the mirrors and the distances involved.
Understanding Mirror Reflections
A concave mirror converges light rays and can produce real or virtual images depending on the object's position. A plane mirror, on the other hand, always produces a virtual image that is the same distance behind the mirror as the object is in front of it.
Given Data
- Curvature radius of the concave mirror: 60 cm
- Object position: Center between the two mirrors
Calculating the Focal Length
The focal length (f) of a concave mirror is given by:
f = -R/2
For a radius (R) of 60 cm, the focal length is:
f = -60 cm / 2 = -30 cm
Image Formation
When the object is placed at the center (30 cm from the concave mirror), the image formed by the concave mirror will be:
Image distance (v) = f = -30 cm
This means the image is formed 30 cm in front of the concave mirror, which is also the same distance from the plane mirror.
Final Image Position
When this image reflects off the plane mirror, it will appear to be 30 cm behind the plane mirror. Therefore, the total distance between the concave mirror and the plane mirror is:
Distance = 30 cm (to the image) + 30 cm (to the plane mirror) = 60 cm
Conclusion
The separation between the two mirrors is therefore 60 cm. Thus, the correct answer is:
D. 60 cm
