Question

A concave spherical mirror has a radius of curvature of magnitude 20.0 cm. (a) Find the location of the image for object distances of (i) 40.0 cm, (ii) 20.0 cm, and (iii) 10.0 cm. For each case, state whether the image is (b) real or virtual and (c) upright or inverted. (d) Find the magnification in each case.

Answer 1

To find the location of the image formed by a concave spherical mirror, use the mirror equation and focal length values. The image is real and inverted for all object distances of 40.0 cm, 20.0 cm, and 10.0 cm. The magnification is calculated using the formula -di/do.

Step-by-step explanation:

To find the location of the image formed by a concave spherical mirror, we can use the mirror equation: 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.

For an object distance of 40.0 cm, substituting the given values into the equation, we find that di = 13.3 cm. The image is real and inverted.

For an object distance of 20.0 cm, we find that di = 6.7 cm. The image is real and inverted.

For an object distance of 10.0 cm, we find that di = 3.3 cm. The image is real and inverted.

The magnification (m) can be calculated using the formula: m = -di/do. For each case, substituting the values, we can find the magnification:

For an object distance of 40.0 cm, m = -0.33.

For an object distance of 20.0 cm, m = -0.67.

For an object distance of 10.0 cm, m = -1.33.

Answer 2

Step-by-step explanation:

It is given that,

Radius of curvature of the mirror, R = 20 cm

So, focal length of the mirror, f = -10 cm

(i) Object distance, u = -40 cm

Using the mirror's formula as :

`(1)/(v)+(1)/(u)=(1)/(f)`

v is the image distance

`(1)/(v)=(1)/(f)-(1)/(u)`

`(1)/(v)=(1)/(-10)-(1)/(-40)`

v = -13.33 cm

Magnification of mirror is calculated as :

`m=(-v)/(u)`

`m=(-(-13.33))/((-40))`

m = -0.33

Since, the magnification is negative, image is real and inverted.

(ii) Object distance, u = -20 cm

Using the mirror's formula as :

`(1)/(v)+(1)/(u)=(1)/(f)`

v is the image distance

`(1)/(v)=(1)/(f)-(1)/(u)`

`(1)/(v)=(1)/(-10)-(1)/(-20)`

v = -20 cm

Magnification of mirror is calculated as :

`m=(-v)/(u)`

`m=(-(-20))/((-40))`

m = -0.5

Since, the magnification is negative, image is real and inverted.

(iii) Object distance, u = -10 cm

Using the mirror's formula as :

`(1)/(v)+(1)/(u)=(1)/(f)`

v is the image distance

`(1)/(v)=(1)/(f)-(1)/(u)`

`(1)/(v)=(1)/(-10)-(1)/(-10)`

v = infinity

Magnification of mirror is calculated as :

magnification = infinity

Hence, this is the required solution.