Question

An object (height=1cm) is placed at 20 cm in front of a concave mirror .Real image formed is at 20cm in front of concave mirror . find the focal length of the mirror .find magnification also.​

Answer 1

The focal length of the concave mirror is -20 cm (negative due to the concave nature of the mirror), and the magnification is -1 .

Step-by-step explanation:

A concave mirror forms real images when the object is located beyond its focal point. In this case, the object is placed at 20 cm in front of the concave mirror, and a real image is formed at 20 cm in front of the mirror. According to the mirror equation
`\( (1)/(f) = (1)/(v) + (1)/(u) \)`, where f is the focal length, v is the image distance, and u is the object distance, we can find the focal length.

Given that v = -20 cm (real image formed on the same side as the incident light) and u = -20 cm (object distance is negative for objects placed in front of the mirror), we can substitute these values into the equation:

`\[ (1)/(f) = (1)/(-20) + (1)/(-20) \]`

Simplifying this expression gives
`\( (1)/(f) = -(1)/(20) \)`. Taking the reciprocal of both sides, we find f = -20 cm. The negative sign indicates the concave nature of the mirror.

The magnification m is given by the formula
`\( m = -(v)/(u) \)`. Substituting the values, we get
`\( m = -((-20))/((-20)) = -1 \)`. The negative magnification indicates an inverted image.