Understanding the Lens Formula with Practice Numericals
Introduction to the Lens Formula
The lens formula is a mathematical relationship used in optics to relate the focal length (f), object distance (u), and image distance (v) for lenses. This formula is crucial in predicting the position and nature of the image formed by lenses, both convex and concave.
The Lens Formula
The lens formula is given by:
1/f = 1/v – 1/u
where:
- f = focal length of the lens
- v = image distance from the lens
- u = object distance from the lens
Note: Sign conventions apply, so it’s essential to use the correct positive or negative signs for each value.
Practice Numericals
Numerical 1: A convex lens has a focal length of 20 cm. An object is placed 40 cm from the lens. Calculate the image distance.
Solution:
1/f = 1/v – 1/u
1/20 = 1/v – 1/40
v ≈ 40 cm
Numerical 2: A concave lens with a focal length of -15 cm has an object placed 30 cm away. Find the image distance.
Solution:
1/f = 1/v – 1/u
1/(-15) = 1/v – 1/30
v ≈ -10 cm
Numerical 3: If an object is placed 10 cm from a convex lens with f = 10 cm, calculate the image distance.
Solution:
1/10 = 1/v – 1/10
v = infinity (image at infinity)
Numerical 4: An object is 25 cm from a convex lens with f = 15 cm. Find the image distance and nature of the image.
Solution:
1/15 = 1/v – 1/25
v ≈ 37.5 cm (real image)
Numerical 5: A concave lens has a focal length of -20 cm. An object is placed 15 cm away. Find the image distance.
Solution:
1/(-20) = 1/v – 1/15
v ≈ -8.57 cm
Numerical 6: A convex lens with f = 30 cm forms an image 45 cm away. Find the object distance.
Solution:
1/30 = 1/45 – 1/u
u ≈ 90 cm
Numerical 7: A concave lens has a focal length of -10 cm. The object is 20 cm away. Calculate the image distance.
Solution:
1/(-10) = 1/v – 1/20
v ≈ -6.67 cm
Numerical 8: For a convex lens with f = 12 cm, an object is placed 30 cm away. Determine the image distance.
Solution:
1/12 = 1/v – 1/30
v ≈ 20 cm
Numerical 9: If a concave lens with f = -25 cm forms an image 12.5 cm away, find the object distance.
Solution:
1/(-25) = 1/12.5 – 1/u
u ≈ 8.33 cm
Numerical 10: A convex lens of focal length 18 cm has an object at 50 cm. Calculate the image distance.
Solution:
1/18 = 1/v – 1/50
v ≈ 28.57 cm
Numerical 11: A concave lens has a focal length of -30 cm, and the object distance is 20 cm. Find the image distance.
Solution:
1/(-30) = 1/v – 1/20
v ≈ -12 cm
Numerical 12: If a convex lens with f = 22 cm creates an image 66 cm away, find the object distance.
Solution:
1/22 = 1/66 – 1/u
u ≈ 33 cm
Numerical 13: An object is 50 cm from a concave lens with f = -25 cm. Find the image distance.
Solution:
1/(-25) = 1/v – 1/50
v ≈ -16.67 cm
Numerical 14: A convex lens with f = 24 cm has an object at 48 cm. Calculate the image distance.
Solution:
1/24 = 1/v – 1/48
v ≈ 48 cm
Numerical 15: For a concave lens with f = -18 cm, an object is placed 18 cm away. Calculate the image distance.
Solution:
1/(-18) = 1/v – 1/18
v ≈ -9 cm
Numerical 16: A convex lens forms an image 24 cm away from an object at 12 cm. Find the focal length.
Solution:
1/f = 1/24 + 1/12
f ≈ 8 cm
Numerical 17: A concave lens forms an image 10 cm away from an object at 15 cm. Find the focal length.
Solution:
1/f = 1/10 + 1/15
f ≈ -6 cm
Numerical 18: A convex lens with f = 15 cm forms an image of an object placed 10 cm away. Calculate the image distance.
Solution:
1/15 = 1/v – 1/10
v ≈ 30 cm
Numerical 19: A concave lens has f = -12 cm, and an object is 6 cm from the lens. Find the image distance.
Solution:
1/(-12) = 1/v – 1/6
v ≈ -4 cm
Numerical 20: A convex lens has a focal length of 25 cm. An object is placed 75 cm away. Find the image distance.
Solution:
1/25 = 1/v – 1/75
v ≈ 37.5 cm
