Question

A concave mirror with a radius of curvature of 20 cm has a focal length of

Answer 1

Answer:

A concave mirror has a radius of curvature of 20 cm. What is it's focal length? If an object is placed 15 cm in front of it, where would the image be formed? What is it's magnification?

The focal length is of 10 cm, object distance is 30 cm and magnification is -2.

Explanation:

Given:

A concave mirror:

Radius of curvature of the mirror, as C = 20 cm

Object distance in-front of the mirror = 15 cm

a.

Focal length:

Focal length is half of the radius of curvature.

Focal length of the mirror =  $\frac{C}{2}$ = 10 cm

According to the sign convention we will put the mirror on (0,0) point, of the Cartesian coordinate open towards the negative x-axis.

Object and the focal length are also on the negative x-axis where focal length and image distance will be negative numerically.

b.

We have to find the object distance:

Formula to be use:

⇒ $\frac{1}{focal\ length}= \frac{1}{image\ distance} + \frac{1}{object\ distance}$

⇒ Plugging the values.

⇒ $\frac{1}{-10} =\frac{1}{image\ distance}+\frac{1}{-15}$

⇒ $\frac{1}{-10} -\frac{1}{-15}=\frac{1}{image\ distance}$

⇒ $\frac{1}{-10} + \frac{1}{15}=\frac{1}{image\ distance}$

⇒ $\frac{-3+2}{30} =\frac{1}{image\ distance}$

⇒ $\frac{-1}{30} =\frac{1}{image\ distance}$

⇒ $-30\ cm=image\ distance$

Image will be formed towards negative x-axis 30 cm away from the pole.

c.

Magnification (m) is the negative ratio of mage distance and object distance:

⇒ $m=-\frac{image\ distance}{object\ distance}$

⇒ $m=-\frac{(-30)}{(-15)}$

⇒ $m=-2$

The focal length of the concave mirror, is of 10 cm, object distance is 30 cm and magnification is -2.