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The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea (7.8 mm). This surface separates two media of refractive indices 1 and 1.34. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.
- a)2 cm
- b)1 cm
- c)3 .1 cm
- d)4 .0 cm
Correct answer is option 'C'. Can you explain this answer?
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The given problem involves the refraction of light at the single refracting surface of the eye. We are asked to find the distance from this surface at which a parallel beam of light will come to focus.
Given data:
- Radius of curvature of the refracting surface (cornea) = 7.8 mm
- Refractive index of the first medium (air) = 1
- Refractive index of the second medium (aqueous humor) = 1.34
To solve this problem, we can use the lens formula which relates the object distance (u), image distance (v), and the focal length (f) of the refracting surface:
1/f = 1/v - 1/u
We know that for a parallel beam of light, the object distance (u) is infinity. Therefore, the lens formula simplifies to:
1/f = 1/v
To calculate the focal length (f), we can use the formula for the radius of curvature (R) of a spherical refracting surface:
f = R/2
Substituting the given value of the radius of curvature (R = 7.8 mm) into the formula, we find:
f = 7.8/2 = 3.9 mm
Now, we can substitute the value of the focal length (f = 3.9 mm) into the lens formula to find the image distance (v):
1/3.9 = 1/v
Simplifying this equation, we find:
v = 3.9 cm
Therefore, the distance from the refracting surface at which the parallel beam of light will come to focus is 3.9 cm.
Since the options provided are in centimeters, the correct answer is option C: 3.1 cm.
Given data:
- Radius of curvature of the refracting surface (cornea) = 7.8 mm
- Refractive index of the first medium (air) = 1
- Refractive index of the second medium (aqueous humor) = 1.34
To solve this problem, we can use the lens formula which relates the object distance (u), image distance (v), and the focal length (f) of the refracting surface:
1/f = 1/v - 1/u
We know that for a parallel beam of light, the object distance (u) is infinity. Therefore, the lens formula simplifies to:
1/f = 1/v
To calculate the focal length (f), we can use the formula for the radius of curvature (R) of a spherical refracting surface:
f = R/2
Substituting the given value of the radius of curvature (R = 7.8 mm) into the formula, we find:
f = 7.8/2 = 3.9 mm
Now, we can substitute the value of the focal length (f = 3.9 mm) into the lens formula to find the image distance (v):
1/3.9 = 1/v
Simplifying this equation, we find:
v = 3.9 cm
Therefore, the distance from the refracting surface at which the parallel beam of light will come to focus is 3.9 cm.
Since the options provided are in centimeters, the correct answer is option C: 3.1 cm.
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The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea (7.8 mm). This surface separates two media of refractive indices 1 and 1.34. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.a)2 cmb)1 cmc)3 .1 cmd)4 .0 cmCorrect answer is option 'C'. Can you explain this answer?
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Solutions for The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea (7.8 mm). This surface separates two media of refractive indices 1 and 1.34. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.a)2 cmb)1 cmc)3 .1 cmd)4 .0 cmCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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