A diverging lens has a radius of curvature of 6 cm. A 2 cm high object is placed 5 cm in front of the lens. Find: Si , Di , and draw the situation.
To find the image distance (Si) and the image height (Hi), we can use the lens formula and the magnification formula:
Lens formula: 1/f = 1/di + 1/do
Magnification formula: m = -Si/So = Hi/Ho
Given:
Radius of curvature (R) = 6 cm (Since it's a diverging lens, the radius of curvature is negative)
Object height (Ho) = 2 cm
Object distance (do) = -5 cm (Since the object is placed in front of the lens, the distance is negative)
First, let's calculate the focal length (f) using the formula:
f = R/2
f = 6 cm / 2
f = 3 cm
Now, let's substitute the values into the lens formula and solve for the image distance (Si):
1/f = 1/di + 1/do
1/3 = 1/di + 1/(-5)
1/di = 1/3 - 1/(-5)
1/di = (5 - 3) / 15
1/di = 2/15
di = 15/2
di = 7.5 cm
The image distance (Si) is 7.5 cm.
Next, let's calculate the magnification (m):
m = -Si/So = Hi/Ho
-7.5/(-5) = Hi/2
m = 1.5 = Hi/2
Hi = 1.5 * 2
Hi = 3 cm
The image height (Hi) is 3 cm.
To draw the situation, draw a horizontal line to represent the principal axis. Mark a vertical line perpendicular to the principal axis to represent the object, with an arrow to indicate the top of the object. Then, draw a second vertical line parallel to the first line to represent the image, again with an arrow to indicate the top of the image. The distance from the object to the lens should be 5 cm, and the distance from the lens to the image should be 7.5 cm. The height of the object should be 2 cm, and the height of the image should be 3 cm.