Question

What does the magnification produced by a spherical mirror represent?

• A. The distance between the mirror and the object
• B. The ratio of the height of the object to the height of the image
• C. The ratio of the height of the image to the height of the object
• D. The size of the mirror

Hint:

Remember the formula: \(m = \frac{h_i}{h_o} = -\frac{v}{u}\).
Image height is always in the numerator, and object height is always in the denominator.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the definition and physical representation of the term "magnification" in the context of spherical mirrors.

Step 2: Key Formula or Approach:
The linear magnification (\(m\)) produced by a spherical mirror is defined by the formula:
\[ m = \frac{\text{Height of image } (h_i)}{\text{Height of object } (h_o)} \]

Step 3: Detailed Explanation:

• Magnification is a dimensionless ratio that indicates how many times the image of an object is enlarged or reduced relative to the actual object.

• It is mathematically defined as the ratio of the height of the image (\(h_i\)) to the height of the object (\(h_o\)).

• It can also be expressed in terms of image distance (\(v\)) and object distance (\(u\)) as:
\[ m = -\frac{v}{u} \]

• If \(|m| \gt 1\), the image is magnified.

• If \(|m| \lt 1\), the image is diminished.

• If \(|m| = 1\), the image is of the same size as the object.

• A positive sign of \(m\) indicates a virtual and erect image, while a negative sign indicates a real and inverted image.


Step 4: Final Answer:
Magnification represents the ratio of the height of the image to the height of the object.