An object which is 3cm high is placed vertically 10cm in front of a concave mirror. If this object produces an image 40cm from the mirror, the height of the...

Answer Details

To solve this problem, we can use the mirror formula: 1/f = 1/v + 1/u where f is the focal length of the mirror, v is the distance of the image from the mirror, and u is the distance of the object from the mirror. We are given u = 10cm and v = 40cm. To find f, we can rearrange the formula: 1/f = 1/v + 1/u 1/f = 1/40 + 1/10 1/f = 0.03 f = 33.33cm Now, we can use the magnification formula: m = -v/u where m is the magnification of the image. Plugging in the values, we get: m = -v/u m = -40/10 m = -4 The negative sign indicates that the image is inverted. Finally, we can use the magnification formula to find the height of the image: m = h'/h where h' is the height of the image and h is the height of the object. Plugging in the values, we get: m = h'/h -4 = h'/3 h' = -12cm Again, the negative sign indicates that the image is inverted. To find the absolute value of the height, we ignore the sign: | h' | = 12cm Therefore, the height of the image is 12cm. Answer is correct.