Question

What is the size of the image formed when the object is at infinity in front of a concave mirror?

• A. Highly magnified
• B. Highly diminished, point-sized
• C. Same size as the object
• D. Inverted and large

Hint:

An object at infinity always forms its image at the focus of a spherical mirror or lens.
The image in this case is always highly diminished (point-sized).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the size of the image created by a concave mirror when the object is positioned at an infinite distance from the mirror.

Step 2: Key Formula or Approach:
We use the fundamental rules of ray optics for spherical mirrors.
When \(u \to -\infty\), we analyze the position and size of the image.

Step 3: Detailed Explanation:

• Light rays originating from an object at infinity travel parallel to each other.

• When these parallel rays are parallel to the principal axis of a concave mirror, they converge at the principal focus (\(F\)) after reflection.

• Let us apply the mirror formula to verify this:
\[ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \]

• As \(u \to -\infty\), \(\frac{1}{u} \to 0\):
\[ \frac{1}{v} + 0 = \frac{1}{f} \implies v = f \]

• The magnification is:
\[ m = -\frac{v}{u} = -\frac{f}{-\infty} \to 0 \]

• A magnification approaching zero indicates that the image size is extremely small compared to the object.

• Therefore, the image formed at the focus is highly diminished and point-sized.


Step 4: Final Answer:
The size of the image is highly diminished, point-sized.