Question

An object is placed at 10 cm in front of a concave mirror. If the image is at 20 cm from the mirror on the same side of the object, then the magnification produced by the mirror is

• A. 3
• B. -0.5
• C. -1
• D. 0.33
• E. -2

Answer 1

Answer: (E)

Magnification of a Concave Mirror 

An object is placed 10 cm in front of a concave mirror. The image is at 20 cm from the mirror on the same side of the object. We need to find the magnification produced by the mirror.

Step 1: Sign Conventions

* Object distance (u): Distance of the object from the mirror. Always taken as negative when the object is in front of the mirror. * Image distance (v): Distance of the image from the mirror. Negative if the image is on the same side as the object (virtual image), positive if on the opposite side (real image).

Step 2: Given Values

* Object distance: \(u = -10 \text{ cm}\) * Image distance: \(v = -20 \text{ cm}\) (since the image is on the same side as the object)

Step 3: Magnification Formula

The magnification (m) is given by:

\(m = -\frac{v}{u}\)

Step 4: Calculate Magnification

Plugging in the values:

\(m = -\frac{-20 \text{ cm}}{-10 \text{ cm}} = -2\)

Conclusion

The magnification produced by the mirror is -2.

Answer 2

We are given:

• Object distance, \( u = -10 \, \text{cm} \) (object in front of the mirror)
• Image distance, \( v = -20 \, \text{cm} \) (image on the same side, so negative for concave mirror)

The magnification \( m \) is given by: \[ m = \frac{v}{u} = \frac{-20}{-10} = 2 \]

But in the options, only -2 is given. This suggests a mistake in sign: for real and inverted images, the magnification is negative. Since the image is real (on the same side as object), the correct magnification is: \[ m = -2 \]

Final Answer: \( \boxed{-2} \)