1. 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
2. A 10-cm high object is placed 60 cm from a 30-cm focal length diverging lens. Determine the image distance, the magnification of the image, the image height, the 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 (h) = 10 cm
The object distance (do) = 60 cm
Wanted : The image distance (di), the magnification of image (m), the image height (hi) and the properties of image
Solution :
Formation of image by diverging lens :
The image distance (di) :
1/di = 1/f – 1/do = -1/30 – 1/60 = -2/60 – 1/60 = -3/60
di = -60/3 = -20 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 = -(-20)/60 = 20/60 = 1/3
The plus sign indicates that the image is upright.
The image 1/3 smaller than the object.
Th image height (hi) :
m = hi / ho
hi = m ho = (1/3)10 = 10/3 = 3.3 cm
The plus sign indicates that the image is upright.
Properties of image
– virtual because the rays do not pass through the image
– upright
– the image smaller than the object
– the image distance smaller than the object distance
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