Where must an object be placed in front of a plus lens in air of focal length 8cm to give an image:
i. 25cm behind the lens?
ii. 25cm in front of the lens?
To determine the placement of an object in front of a plus lens to give a specific image position, 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, and
- u is the object distance from the lens.
Let's calculate the required object distance for each scenario:
i. To place the object in front of the plus lens and obtain an image 25cm behind the lens:
u = 1/(1/f - 1/v)
= 1/(1/8 - 1/-25) [Substituting f = 8cm and v = -25cm]
= 1/(0.125 + 0.04)
= 1/0.165
= 6.06 cm (approximately)
Therefore, the object must be placed approximately 6.06 cm in front of the lens to obtain an image 25 cm behind it.
ii. To place the object in front of the plus lens and obtain an image 25cm in front of the lens:
u = 1/(1/f - 1/v)
= 1/(1/8 - 1/25) [Substituting f = 8cm and v = 25cm]
= 1/(0.125 - 0.04)
= 1/0.085
= 11.76 cm (approximately)
Therefore, the object must be placed approximately 11.76 cm in front of the lens to obtain an image 25 cm in front of it.