Hello,
I need some help with the following question.
Thank You,
When an object is placed 8mm from a concave spherical mirror, a clear image can be projected on a screen 16 mm in front of the mirror. If the object has a height of 4 mm, the height of the image is?
I think it's 2 mm or 8 mm I am not certain.
choses:
2 mm
4 mm
8 mm
12 mm
The magnification ratio is
D(image)/D(object) = 2
If the object is 4mm high, the image height is twice that.
m=I/o = 16mm/8mm=2
m=hi/ho
hi-m*ho=2*4mm=8mm
To find the height of the image formed by a concave mirror, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the mirror,
- v is the image distance from the mirror (also called the virtual image distance),
- u is the object distance from the mirror.
We are given two distances in the question:
1. The object distance (u) = 8 mm (negative since the object is in front of the mirror).
2. The image distance (v) = -16 mm (negative since the image is formed on the same side of the mirror as the object).
Using these values in the mirror formula:
1/f = 1/(-16) - 1/8
1/f = -1/16 - 1/8
1/f = - (1/16 + 2/16)
1/f = -3/16
To simplify the equation, we can take the reciprocal of both sides:
f = -16/3 mm
The negative sign indicates that the concave mirror is diverging (also known as a convex mirror).
Now, to find the height of the image (h'), we can use the magnification formula:
m = h'/h = -v/u
Where:
- h' is the height of the image,
- h is the height of the object (given as 4 mm),
- v is the image distance from the mirror (negative),
- u is the object distance from the mirror (negative).
Plugging in the values:
m = h'/4 = -(-16/8) = 16/8 = 2
Solving for h':
h' = (2)(4) = 8 mm
Therefore, the height of the image is 8 mm.
So, from the given choices, the correct answer is 8 mm.