Question

Magnification produced by a rear view mirror fitted in vehicles:

• A. is less than one
• B. is more than one
• C. is equal to one
• D. can be more than or less than one depending upon the position of the object in front of it

Hint:

Rear-view mirror = Convex mirror.
Convex mirrors always produce diminished images (\(h_i \lt h_o\)).
Therefore, the magnification \(m\) is always positive and less than 1 (\(m \lt 1\)).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks about the magnification value produced by the rear-view mirrors installed in vehicles.

Step 2: Key Formula or Approach:
Rear-view mirrors in vehicles are convex mirrors.
Linear magnification (\(m\)) is defined as:
\[ m = \frac{\text{Height of image } (h_i)}{\text{Height of object } (h_o)} \]

Step 3: Detailed Explanation:

• Convex mirrors are used as rear-view mirrors because they always form an erect, virtual, and diminished (smaller) image of objects, regardless of how far the objects are.

• Since the image formed is always smaller than the actual object:
\[ h_i \lt h_o \]

• Substituting this into the magnification formula:
\[ m = \frac{h_i}{h_o} \lt 1 \]

• Since both the object and virtual image are erect (above the principal axis), both heights are positive, meaning \(m\) is a positive number less than 1.

• This diminished image allows a convex mirror to provide a much wider field of view of the traffic behind compared to a plane mirror.


Step 4: Final Answer:
The magnification produced by a rear view mirror is less than one.