For a human eye, where u is the distance of an object from the eye, f is the focal length of the lens and v is the distance of image from the eye, which is the correct schematic graph?
Given:
For a human eye, where u is the distance of an object from the eye, f is the focal length of the lens, and v is the distance of the image from the eye.
Concept Used:
The lens formula for a thin lens is given by:
1/f = 1/v + 1/u
Where:
- u is the object distance (measured from the lens)
- v is the image distance (measured from the lens)
- f is the focal length of the lens
Calculation:
We need to plot the graph based on the lens formula:
⇒ If we rearrange the lens formula, we get:
1/v = 1/f - 1/u
⇒ As u changes, v will change accordingly to satisfy the lens formula. The relationship between u and v is hyperbolic.
Let's consider a few cases:
⇒ When u = ∞ (object is at infinity),
1/v = 1/f - 0
v = f
⇒ When u = f (object is at the focal length),
1/v = 1/f - 1/f
v = ∞
⇒ When u < f (object is between the lens and the focal point),
v is negative indicating a virtual image.
Based on this, the correct schematic graph is option 1, which shows the hyperbolic relationship between u and v.
∴ The correct answer is option 1.
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