numericals on concave lens
Answers
A 5-cm high object is placed 15 cm from a 30-cm focal length diverging lens. Determine the image distance, the magnification of the image, the image height, and properties of the image.
Known :
The focal length (f) = -30 cm
The minus sign indicates that the focal point is virtual or the rays do not pass through the point.
The object height (ho) = 5 cm
The object distance (do) = 15 cm
Wanted: The image distance (di), the magnification of image (m), the image height (hi) and the properties of the image.
Solution :
Formation of image by diverging lens :
The image distance (di) :
1/di = 1/f – 1/do = -1/30 – 1/15 = -1/30 – 2/30 = -3/30
di = -30/3 = -10 cm
The minus sign indicates that the image is virtual or the rays do not pass through the image.
The magnification of image (m) :
m = – di / do = -(-10)/15 = 10/15 = 2/3
The plus sign indicates that the image is upright.
The image 2/3 smaller than the object.
The image height (hi) :
m = hi / ho
hi = m ho = (2/3)5 = 10/3 = 3.3 cm
The plus sign indicates that the image is upright.
The properties of the image :
The properties of the image formed by a diverging mirror :
– virtual
– upright
– the image smaller than the object
– the image distance smaller than the object distance
Answer:
1. An object is placed 10 cm from a concave mirror. The focal length is 5 cm. Determine (a) The image distance (b) the magnification of image
Known :
The focal length (f) = 5 cm
The object distance (do) = 10 cm
2. A 5-cm-high object is placed in front of a concave mirror with a radius of curvature of 20 cm. Determine the image height if the object distance is 5 cm, 15 cm, 20 cm, 30 cm.
Known :
The radius of curvature (r) = 20 cm
The focal length (f) = R/2 = 20/2 = 10 cm
The object height (ho) = 5 cm
3.. An image an by a concave mirror is 4 times greater than the object. If the radius of curvature 20 cm, determine the object distance in front of the mirror!
Known :
The magnification of image (m) = 4
The radius of curvature (r) = 20 cm
The focal length (f) = r/2 = 20/2 = 10 cm