A CONVEX LENS PRODUCES O REAL AND INVERTED
IMAGE 2.5 TIMES MAGNIFIED AT A DISTANCE OF 25CM FROM THE LENS.CALCULATE THE FOCAL LENGTH OF THE LENS,
Thanks
Wanda
To calculate the focal length of the convex lens, we can use the lens formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens
- v is the image distance from the lens (in meters)
- u is the object distance from the lens (in meters)
Given that the image is real, inverted, and magnified 2.5 times, we can determine the values for v and u as follows:
Magnification (M) = -v/u
Since the image is 2.5 times magnified, we have:
2.5 = -v/u
Now, we are given that the image distance (v) is 25 cm, which is equal to 0.25 meters. Plugging this value into the equation, we get:
2.5 = -0.25/u
Simplifying, we have:
u = -0.25/2.5
u = -0.1 meters
With this information, we can now substitute the values of v and u into the lens formula:
1/f = 1/v - 1/u
1/f = 1/0.25 - 1/(-0.1)
Simplifying further:
1/f = 4 - (-10)
1/f = 14
To find the focal length, we take the reciprocal of both sides:
f = 1/14
f ≈ 0.071 meters
Therefore, the focal length of the convex lens is approximately 0.071 meters (or 7.1 cm).
2.5x/25 = x/do
do=25x/2.5x=10cm
1/di+1/do=1/f
1/25 + 1/10 =1/f
7/50=1/f
f=50/7=7.14 cm