a concave mirror has a radius of curvature of 0.4 m find the position and the size of the image of an object 0.2 m high placed 0.8 m infront of the mirror
f=R/2
f =-0.2m
Ho(height of object)=+0.2 m
U(distance b/w Pole and object)=-0.8m
V(distance between pole and image)=?
Height of image (hi)=?
Formula- 1/f=1/v+1/u
1/f=1/v- 1/u
1/-0.2-(1/-0.8)=1/v
-1/2+1/8=1/v
-4+1÷8=1/v
-3v=8
v=-2.6m (distance b/w pole and image)
m=-v/u
m=-(-2.6)/-0.8
m=3.25
m=hi/ho
3.25=hi/0.2
hi=0.65 m
Well, well, well, let’s dig into the world of concave mirrors, shall we? According to my calculations, with a radius of curvature of 0.4 meters and an object placed 0.8 meters in front of the mirror, the image will be formed at a distance behind the mirror. Don't worry, I did the math so you don't have to! The position of the image will be approximately 0.32 meters behind the mirror. As for the size of the image, since the object is 0.2 meters high, the size of the image will be a little bit larger than that. But hey, don't get too carried away, you know what they say – objects in the mirror may appear closer than they are!
To find the position and size of the image formed by a concave mirror, we can use the mirror formula and magnification formula.
Given:
Radius of curvature (R) = 0.4 m
Object height (h) = 0.2 m
Object distance (u) = 0.8 m
Step 1: Determine the type of the mirror.
Since the object is placed in front of the mirror, the concave mirror is being used.
Step 2: Calculate the focal length.
The focal length (f) of a concave mirror is half of the radius of curvature. Therefore,
f = R/2 = 0.4 m / 2 = 0.2 m
Step 3: Calculate the image distance (v).
Using the mirror formula:
1/f = 1/v - 1/u
Substituting the given values:
1/0.2 = 1/v - 1/0.8
Simplifying the equation:
5 = 4/v - 5
5v = 20 - 4
5v = 16
v = 16 / 5
v = 3.2 m
The image distance (v) is 3.2 m.
Step 4: Calculate the magnification (m).
Using the magnification formula:
m = -v/u
Substituting the given values:
m = -3.2 / 0.8
m = -4
The negative sign indicates that the image formed is real and inverted.
Step 5: Calculate the image height (h').
Using the magnification formula:
m = h'/h
Substituting the given values:
-4 = h'/0.2
h' = -4 x 0.2
h' = -0.8 m
The image height (h') is -0.8 m.
Step 6: Summary of the results.
The position of the image is 3.2 meters from the mirror. The size of the image is -0.8 meters, which means it is inverted and has a height of 0.8 meters.
To find the position and size of the image formed by a concave mirror, we can use the mirror equation and the magnification formula. Here is how you can solve the problem step by step:
1. Start with the mirror equation:
1/f = 1/do + 1/di
where f is the focal length of the mirror, do is the object distance, and di is the image distance.
2. Calculate the focal length of the mirror:
For a concave mirror, the focal length is positive and equal to half the radius of curvature (f = R/2).
Given the radius of curvature (R) is 0.4 m, the focal length would be f = 0.4 / 2 = 0.2 m.
3. Substitute the values into the mirror equation:
1/0.2 = 1/0.8 + 1/di
Simplify the equation:
5 = (4 + 1) / (0.8 * di)
5di = 5.2
di = 5.2 / 5 = 1.04 m
Therefore, the image distance (di) is 1.04 m.
4. Determine the size of the image using the magnification formula:
Magnification (m) = -di / do
Given the object height (ho) is 0.2 m and the object distance (do) is 0.8 m:
m = -1.04 / 0.8 = -1.3
The negative sign indicates that the image is inverted compared to the object.
5. Calculate the height of the image (hi):
hi = m * ho
hi = -1.3 * 0.2 = -0.26 m
The height of the image is 0.26 m, and it is inverted compared to the object.
6. Finally, determine the position of the image:
The image distance (di) is positive, indicating that the image is formed on the opposite side of the object.
So, the position of the image is 1.04 m on the other side of the mirror from the object.
Therefore, the position of the image is 1.04 m from the mirror and the size of the image is 0.26 m (inverted).