When an object is placed at a distance of 50 cm from a concave spherical mirror, the magnification produced is -1/2, where should the object be placed to get a magnification of -1/5 ?
Answers
Answer:
Explanation:
It may seem very difficult to figure out but you just have to read all the hints given and it will start to make sense. The calculation part is the easiest part. To start, since you are given that the magnification is negative means the image is inverted so that would make it a real image instead of virtual. A real image would be on the same side of the mirror as the object. Also the magnitude of the magnification is the ratio of the respective image and object distances; hence the image distance must be half the distance of the object in order to get an image half the size. The image turns out to be a little more than the focal point away from front of concave mirror. Moving the object farther way would make the image smaller and come closer to the focal point. To get a magnification of -1/5, the image distance would be 1/5 the distance of the object (i.e. the object is five times farther away than the image).
Since we knew the object distance in the first case to be 50cm, then we know that half of that is 25cm and the image distance. Plugging into lens equation gives 16.67 cm for the focal length. It also turns out that the object distance equals the focal point times the reciprocal magnification plus 1, or times 6. So that would give an object distance of 100cm (and image distance 20cm).