what would be the distance from the image to the mirror if the imge form the object to the mirror is 20cm and the focal length is 10 cm
To find the distance from the image to the mirror in a mirror setup, we can use the mirror formula:
\( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \)
Where:
- \( f \) is the focal length of the mirror,
- \( d_o \) is the object distance,
- \( d_i \) is the image distance.
In this case, the object distance (\( d_o \)) is given as 20 cm and the focal length (\( f \)) is 10 cm. We want to find the image distance (\( d_i \)).
Substituting the given values into the formula:
\( \frac{1}{10} = \frac{1}{20} + \frac{1}{d_i} \)
To solve for \( d_i \), we can rearrange the equation:
\( \frac{1}{d_i} = \frac{1}{10} - \frac{1}{20} \)
Simplifying the equation:
\( \frac{1}{d_i} = \frac{2 - 1}{20} = \frac{1}{20} \)
Taking the reciprocal of both sides:
\( d_i = 20 \) cm
Therefore, the distance from the image to the mirror is 20 cm.