a 5cm object is placed 50cm grom a converging mirror whose focal length is 20 cm. find the position and size of the image. Draw a ray diagram.
I can't draw a ray diagram here, but you need to do that. http://www.physicsclassroom.com/class/refln/Lesson-3/Ray-Diagrams-Concave-Mirrors
To find the position and size of the image formed by a converging mirror, you can use the mirror equation and magnification formula.
The mirror equation is given by:
1/f = 1/di + 1/do
where:
- f is the focal length of the mirror
- di is the image distance (position of the image)
- do is the object distance (distance of the object from the mirror)
The magnification formula is given by:
magnification (m) = -di/do
where:
- di is the image distance
- do is the object distance
Given:
f = +20 cm (converging mirror with positive focal length)
do = +50 cm (since the object is placed at a distance of 50 cm from the mirror)
We can substitute these values into the mirror equation to find di (the image distance):
1/20 = 1/di + 1/50
To solve for di, we may take the reciprocal of both sides of the equation:
20 = di/50 + 1
Simplifying the equation, we get:
20 = (di + 50)/50
Now, cross-multiply the equation:
20 * 50 = di + 50
1000 - 50 = di
di = 950 cm
The negative sign indicates that the image formed is real and located on the same side as the object.
Now, let's calculate the magnification (m):
magnification (m) = -di/do
m = -(950/50)
m = -19
Here, the negative sign indicates that the image is inverted compared to the object.
So, the image is formed at a distance of 950 cm (9.5 meters) from the mirror, and it is inverted.
To draw a ray diagram, you can start by drawing the converging mirror with its focal point. Then, draw a straight line to represent the object, placed at a distance of 50 cm (do) from the mirror. Draw two rays from the object: one parallel to the principal axis, and another ray passing through the focal point. Extend these rays behind the mirror. The intersection point of these rays will give you the position and size of the image.