Answer: a. 53cm b. Diverging c. 0.02dioptres
Explanation:
Since the person in question cannot see far object clearly, it shows that the individual is suffering from myopia (short sightedness).
If the object distance (u) is 53cm. for the person to be able to see far way, it means the image must be at infinity. This shows image distance v is infinity. Using the lens formula
1/f = 1/u+1/v
1/f = 1/53 + 1/Infinity
1/f = 1/53 + 0
f=53cm
b) The lens used is concave lens (diverging lens) to diverge all rays outwards
c) Power of a lens P will be 1/53.
P = 0.02dioptres
The focal length of the lens is 53 cm, the lens is diverging type, and the power of the lens is 0.02 dioptres.
The converging lens can be defined as when light approaches the lens it converges the light rays whereas the diverging lens diverse the coming light rays towards the lens.
We have the farthest distance a person can see without visual aid
= 53 cm
We know the lens formula:
[tex]\rm \frac{1}{f} = \frac{1}{u} +\frac{1}{v}[/tex]
Where f is the focal length
u is the object's distance from the lens
v is the image distance from the lens
We have u = 53 cm and
v = ∞ ( Since the person can see farthest ie. the image will be at infinity)
[tex]\rm \frac{1}{f} = \frac{1}{53} +\frac{1}{\infty}\\\\\rm \frac{1}{f} = \frac{1}{53} + 0[/tex]
f = 53 cm
To diverge all rays outwards, a diverging lens will be utilized.
[tex]\rm Power \ of \ the \ lens = \frac{1}{f}[/tex]
P = 1/53
P = 0.018 dioptres or
P ≈ 0.02 dioptres
Thus, the focal length of the lens is 53 cm, the lens is diverging type, and the power of the lens is 0.02 dioptres.
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