An object is placed at a distance of 10 cm in from of a concave mirror. Its image is formed ill a distance at 15 cm on the same side. The focal length of the mirror is:

Correct option is C

Correct Answer: C - -6 cm

Explanation:

The formula for a spherical mirror is:

​$$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$​​

Where:

• f = focal length
• u = object distance (negative for concave mirror as it is in front of the mirror)
• v = image distance (negative for real image as it is on the same side as the object)

Given:

• u=−10 cm (object distance)
• v=−15 cm (image distance)

Substitute the values into the formula:

​$$\frac{1}{f} = \frac{1}{u}\ + \frac{1}{v}\\ \ \\\frac{1}{f} = \frac{1}{-10} + \frac{1}{-15}\\ \ \\ \frac{1}{f} = -\frac{1}{10} - \frac{1}{15}$$​​

Find the common denominator:

​$$\frac{1}{f} = -\left(\frac{3}{30} + \frac{2}{30}\right)\ \\ \ \\ \frac{1}{f} = -\frac{5}{30}$$​​

Simplify:

f=−6 cm

Information Booster:

•  A negative focal length indicates the mirror is concave.
•  For concave mirrors, a real and inverted image forms on the same side as the object when the object is placed beyond the focal point.
•  The formula applies universally to concave and convex mirrors, with appropriate sign conventions.
• The focal length is half the radius of curvature (f=R/2).
  ● In this case, the mirror forms a real image, which is always inverted for concave mirrors.