Question

An object stands on the central axis of a spherical mirror. The object distance is 15.0 cm, the type of mirror is concave, and the magnitude of the focal length is 10.0 cm. (a) Sketch a ray-tracing diagram depicting the size and location of the image. Calculate (b) the image distance and (c) the magnification. (d) Is this image real or virtual?

Answer 1

b.v=-30 cm

c.m=-2

d.Real

Step-by-step explanation:

We are given that

Object distance =u=-15 cm

Focal length of concave mirror=f=-10 cm

Using mirror formula

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

Substituting the values then we get

`(1)/(-10)=(1)/(-15)+(1)/(v)`

`(1)/(v)=(1)/(-10)+(1)/(15)`

`(1)/(v)=(-3+2)/(30)`

`(1)/(v)=(-1)/(30)`

v=-30 cm

Hence, the image distance =-30 cm

c.Magnification formula =
`-(v)/(u)`

Substitute the value then we get

m=
`-(-30)/(-15)=-2`

The magnitude of magnification is greater than 1 therefore, the image is larger than the object.

The magnification is negative therefore, the image is inverted compared to the object.

d.The image is real because image formed inverted and real in concave mirror.