QuestionMay 26, 2025

A candle is placed at a distance of 15 cm from of a concave mirror with a focal length of 5 cm. The candle is 8 cm tall. Where is the image located? square

A candle is placed at a distance of 15 cm from of a concave mirror with a focal length of 5 cm. The candle is 8 cm tall. Where is the image located? square
A candle is placed at a distance of 15 cm from of a concave mirror with a focal length
of 5 cm. The candle is 8 cm tall.
Where is the image located?
square

Solution
4.4(237 votes)

Answer

The image is located at 7.5 cm in front of the mirror. Explanation 1. Use Mirror Formula The mirror formula is **\frac{1}{f} = \frac{1}{v} + \frac{1}{u}**, where f is the focal length, v is the image distance, and u is the object distance. Here, f = -5 cm (concave mirror) and u = -15 cm (object distance is negative for mirrors). 2. Substitute Values Substitute f = -5 cm and u = -15 cm into the formula: \frac{1}{-5} = \frac{1}{v} + \frac{1}{-15}. 3. Solve for Image Distance v Simplify to find v: \frac{1}{v} = \frac{1}{-5} + \frac{1}{15} = \frac{-3 + 1}{15} = \frac{-2}{15}. Thus, v = -\frac{15}{2} = -7.5 cm.

Explanation

1. Use Mirror Formula<br /> The mirror formula is **$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$**, where $f$ is the focal length, $v$ is the image distance, and $u$ is the object distance. Here, $f = -5$ cm (concave mirror) and $u = -15$ cm (object distance is negative for mirrors).<br />2. Substitute Values<br /> Substitute $f = -5$ cm and $u = -15$ cm into the formula: $\frac{1}{-5} = \frac{1}{v} + \frac{1}{-15}$.<br />3. Solve for Image Distance $v$<br /> Simplify to find $v$: $\frac{1}{v} = \frac{1}{-5} + \frac{1}{15} = \frac{-3 + 1}{15} = \frac{-2}{15}$. Thus, $v = -\frac{15}{2} = -7.5$ cm.
Click to rate:

Similar Questions