1)An object of 20mm high is placed 60mm in front of a mirror of the focal length 20mm find the position of the image if the mirror is convex and concave
2) a n object is placed in front of a concave mirror of the focal length 16mm the image formed has magnification of 4 find the position of the object if the image is
A)real
B) virtual
I don't have any idea about this because I don't know
I want answers of my questions
To determine the position of the image formed by a mirror, we can use the mirror formula:
1/f = 1/u + 1/v,
where f is the focal length of the mirror, u is the object distance (distance of the object from the mirror), and v is the image distance (distance of the image from the mirror).
Let's solve each question step by step:
1) For a convex mirror:
Given:
f = 20mm (focal length)
h = 20mm (object height)
u = -60mm (negative since the object is placed in front of the mirror)
We need to find v (image distance).
First, let's convert u to positive:
u = -60mm ==> u = 60mm
Now, plug these values into the mirror formula:
1/20 = 1/60 + 1/v
Simplifying the equation:
1/v = 1/20 - 1/60
1/v = (3 - 1)/60
1/v = 2/60
1/v = 1/30
Therefore, the image distance (v) for a convex mirror is 30mm in front of the mirror.
2) For a concave mirror:
Given:
f = -16mm (focal length)
m = 4 (magnification)
We need to find u (object distance) for different scenarios (real and virtual images).
A) Real Image:
For a real image, the magnification (m) is positive.
Using the magnification formula: m = -v/u, we can find v (image distance) as -4u.
Now, substituting the values into the mirror formula:
1/-16 = 1/u + 1/-4u
Simplifying the equation:
-1/16 = 1/u - 1/4u
-1/16 = (4 - 1)/(4u)
-1/16 = 3/(4u)
Cross-multiplying the equation:
-3u = 16*4
-3u = 64
u = -64/3
Therefore, the object distance (u) for a real image is approximately -21.33mm in front of the concave mirror.
B) Virtual Image:
For a virtual image, the magnification (m) is negative.
Again, we can use the magnification formula: m = -v/u, but this time, m = -4.
Substituting the values into the mirror formula:
1/-16 = 1/u - 1/-4u
Simplifying the equation:
-1/16 = 1/u + 1/4u
-1/16 = (4 + 1)/(4u)
-1/16 = 5/(4u)
Cross-multiplying the equation:
-5u = 16*4
-5u = 64
u = -64/5
Therefore, the object distance (u) for a virtual image is approximately -12.8mm in front of the concave mirror.