Suppose we wish to project an image onto a screen, so that it can be viewed by a
ID: 1519021 • Letter: S
Question
Suppose we wish to project an image onto a screen, so that it can be viewed by an audience. We will project the image by using a spherical mirror.
(a) What type of image will be projected onto the screen? Why? (b) What type of curved mirror should we use? Why?
(c) Suppose we want the focal length to be 10 cm. What is the radius of curvature of the mirror?
(d) Suppose the image is 10 m from the mirror. Where should the object be located?
(e) Draw a ray diagram which shows the character of the image. (It does not need to be drawn to scale but it should be neat and clear.)
Explanation / Answer
(a) Inverted Image will be projected on screen. Image formed on screen is a real image and it is of a real object placed in front of mirror. Real image of real object is alway inverted, wheather it is formed by a mirror or lens.
We can also understand it through path of a ray. Let us say an object is placed above the principal axis. Ray from this object at pole of mirror, will be moving below the principal axis after reflection. All the rays starting from object meet at the position of image, so this ray will also be at image. Hence mage will be below the principal axis and image formed will be inverted.
(b) We should use Concave mirror. Convex mirror forms virtual image for all positions of real object. Concave miror forms real image of objects placed beyond focus of mirror. As we want to project image on screen, it has to be real and hence mirror should be concave.
(c) Focal length of a mirror is half of radius of curvature. Hence radius of curvature of mirror should be 20 cm.
(d) To get position of object we use mirror formula 1/v + 1/u = 1/f
using sign convention that all distances in the direction of incident rays as +ve and opposite distances as -ve, we have f = - 10 cm v = - 1000 cm ( real image is always formed in front of mirror )
Substituting values in above equation we get u = - 10.10
Hence object should be placed at distance of 10.1 cm from mirror.