Question

A concave mirror has a focal length of \( 10 \, \text{cm} \). An object is placed at a distance of \( 15 \, \text{cm} \) from the mirror. Calculate the position of the image formed.

• A. \( 30 \, \text{cm} \) (real and inverted)
• B. \( 5 \, \text{cm} \) (virtual and erect)
• C. \( 10 \, \text{cm} \) (real and inverted)
• D. \( 20 \, \text{cm} \) (virtual and erect)

Hint:

For a concave mirror, if the object is placed outside the focal point, the image formed will be real and inverted. If placed inside the focal point, the image will be virtual and erect.

Answer 1

The Correct Option is A

The mirror equation relates the object distance \( u \), the image distance \( v \), and the focal length \( f \) of a mirror: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] Where: - \( f = -10 \, \text{cm} \) (focal length of the concave mirror, negative for concave mirrors), - \( u = -15 \, \text{cm} \) (object distance, negative because the object is in front of the mirror), - \( v \) is the image distance (to be determined). Rearranging the mirror equation: \[ \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \] Substitute the known values: \[ \frac{1}{v} = \frac{1}{-10} - \frac{1}{-15} \] \[ \frac{1}{v} = -\frac{1}{10} + \frac{1}{15} = -\frac{3}{30} + \frac{2}{30} = -\frac{1}{30} \] Thus: \[ v = -30 \, \text{cm} \] The negative sign indicates that the image is formed on the same side as the object, meaning it is a real and inverted image. The position of the image is \( 30 \, \text{cm} \) from the mirror.