Question

Select the correct statement about the magnitude of the magnification of a concave mirror if the object is beyond the center of curvature C (do > r).

A) The magnitude of the magnification of a concave mirror is equal to 1.
B) The magnitude of the magnification of a concave mirror is greater than 1.
C) The magnitude of the magnification of a concave mirror is less than 1.

Answer 1

The correct statement for the magnitude of magnification of a concave mirror, when the object is beyond the center of curvature, is that it is less than 1, indicating the image formed is real, inverted, and smaller than the object. So the correct option is C.

Step-by-step explanation:

The correct statement about the magnitude of the magnification of a concave mirror when the object is beyond the center of curvature (do > r) is "The magnitude of the magnification of a concave mirror is less than 1." This is because when an object is located beyond the center of curvature, the image formed by a concave mirror is real, inverted, and smaller than the object. Hence, the magnification, which is the ratio of the image size to the object size, is positive but less than 1.

When dealing with concave mirrors, it is important to note that different object positions result in different types of images, depending on the object's distance relative to the mirror's focal length and center of curvature. If the object distance is greater than the radius of curvature, the image formed is smaller than the object, leading to a magnification of less than 1.

Answer 2

c) The magnitude of the magnification of a concave mirror is less than 1

Step-by-step explanation:

we know

the mirror formula is given as:

`(1)/(v)+(1)/(u)=(2)/(r)` ..............(1)

also

magnification (m) of mirror is given as:

`m=(-v)/(u)` . ..... (2)

where,

v = image distance

u = object distance

r = Radius of curvature of the mirror

Now

from (2)

`v=-mu`

substituting in (1), we get

`(1)/(u)((1)/(-m)+1)=(2)/(r)`

or

`(1)/(2)(1-(1)/(m))=(u)/(r)` ..............(3)

now it is given that object is beyond the center of the the curvature

thus,

⇒
`(u)/(r)>1` ................(4)

comparing the (3) and (4), we have

`(1)/(2)(1-(1)/(m))>1`

or

`(1-(1)/(m))>2`

or

`-(1)/(m)>2-1`

or

`-(1)/(m)>1`

⇒
`m<-1`

Hence, the magnification is less than 1