A concave mirror has a radius of curvature of 0.20m. if an image is placed 0.25m from the mirror, find the distance and nature of the image

Data

1/2(r)
I/2(0.2)=0.1
F=0.1×100=10
U=0.25×100=25
V=?
Soln:
a.V=uf/u-f
V=25×10/25-10
V=250/15V=16.66 or 16.7cm
b. The nature of the image is real

Well, well, well, we have a concave mirror and a radius of curvature of 0.20m. Now let's see what sort of image we can conjure up.

The distance of the image is given as 0.25m. Hocus pocus, let me do some calculations.

Now, when the object is placed beyond the focal point of a concave mirror, we get a real and inverted image. So, let's figure out where our dear little image is hiding.

The formula we'll use is 1/f = 1/v - 1/u. Don't worry, we'll make it through this math magic trick together.

Plugging in the values, we get 1/0.20 = 1/v - 1/0.25. Let's simplify this.

5 = 4/v - 4/0.25. Hocus pocus, let's mix things up a bit more.

5 = 4/v - 16. Oh, look at that!

Now, if we bring -16 to the other side, and simplify, we get 4/v = 5 + 16 = 21.

If we flip the equation upside down, we get v = 1/21. So, our distance of the image is approximately 0.048m.

As for the nature of the image, since it's a real image formed by a concave mirror, we can safely say that it is inverted. No need for magic tricks to figure that one out!

Abracadabra!

To find the distance and nature of the image formed by a concave mirror, we can use the mirror equation:

(1/f) = (1/do) + (1/di)

where:
f = focal length of the mirror
do = object distance
di = image distance

The focal length (f) of a concave mirror is related to the radius of curvature (R) by the formula: f = R/2.

Given:
Radius of curvature = 0.20 m
Object distance (do) = 0.25 m

We can substitute these values into the formula to find the image distance (di):

f = R/2 = 0.20/2 = 0.10 m

Using the mirror equation:

(1/0.10) = (1/0.25) + (1/di)

Simplifying the equation:

10 = 4 + (1/di)

Subtracting 4 from both sides:

6 = 1/di

Taking the reciprocal of both sides:

di = 1/6 = 0.1667 m

The distance of the image (di) is approximately 0.1667 m.

Now, we need to determine the nature of the image. It will be either real or virtual, and either erect or inverted.

Since the image distance (di) is positive, the image formed by the concave mirror is real. Since the image distance is also less than the object distance, the image will be inverted.

Therefore, the distance of the image is approximately 0.1667 m, and the image is real and inverted.

To find the distance and nature of the image formed by a concave mirror with a given radius of curvature and object distance, we can use the mirror equation:

1/f = 1/di + 1/do

where f is the focal length of the mirror, di is the image distance, and do is the object distance.

First, let's find the focal length of the concave mirror. The focal length (f) of a concave mirror can be found using the formula:

f = R / 2

where R is the radius of curvature of the mirror. In this case, the radius of curvature is given as 0.20m. Substituting this value:

f = 0.20 / 2
f = 0.10m

Now, we have the focal length as 0.10m.

Next, we can substitute these values into the mirror equation to find the image distance (di):

1/0.10 = 1/di + 1/0.25

Simplifying the equation:

10 = 1/di + 4

Rearranging the equation:

1/di = 10 - 4
1/di = 6

di = 1/6
di = 0.17m

The image distance (di) is 0.17m.

To determine the nature of the image, we need to consider the sign conventions. In this case, since the image distance (di) is positive, the image is formed on the same side of the mirror as the object. This indicates that the image is a real image.

Therefore, the distance of the image formed by the concave mirror is 0.17m, and the nature of the image is real.