An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. The magnification is:

CONCEPT:

Convex mirror: 

• The mirror in which the rays diverges after falling on it is known as the convex mirror.
  • Convex mirrors are also known as a diverging mirror.
  • The focal length of a convex mirror is positive according to the sign convention.
• Mirror Formula: The following formula is known as the mirror formula:

\(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\)

where f is focal length v is the distance of the image from the mirror, and u is the distance of the object from the mirror.​

Linear magnification (m):

• It is defined as the ratio of the height of the image (hi) to the height of the object (ho).

\(m = \frac{{{h_i}}}{{{h_o}}}\)

• The ratio of image distance to the object distance is called linear magnification.

\(m = \frac{{image\;distance\;\left( v \right)}}{{object\;distance\;\left( u \right)}} = - \frac{v}{u}\)

• A positive value of magnification means a virtual and erect image.
• A negative value of magnification means a real and inverted image.

CALCULATION:

• Given -  Object distance (U) = -10 cm and Focal length (f) = 15 cm
• The mirror formula is given by

\(\Rightarrow \frac{1}{f} =\frac{1}{V}+\frac{1}{U}\)

\(\Rightarrow\frac{1}{15} =\frac{1}{V}-\frac{1}{10}\)

\(\Rightarrow\frac{1}{V}=\frac{1}{10}+\frac{1}{15}\)

\(\Rightarrow V=\frac{25}{150} = 6cm\)

• The magnification of a mirror is 

​\(m=-\frac{V}{U}\)​​

\(\Rightarrow m=-\frac{V}{U} =-\frac{6 cm }{-10 cm} =+0.6\)

• The magnification of the object is + 0.6.