Question

An object is placed 9.30 cm in front of the cornea. (The cornea is thin ans has approximately parallel sides so that the reflection that occurs as light travels from air to cornea to aqueous humor is essentially the same as though the aqueous humor were directly in contact with the air. The aqueous humor has index of refraction n = 1.34 and the radius of curvature of cornea is 7.8 mm.)

(a) What is the image distance for the image formed by the cornea alone?

Answer 1

The image distance formed by the cornea alone is 0.0933 cm.

Step-by-step explanation:

When light travels from air into a medium with a different refractive index, such as from air (n ≈ 1) to the aqueous humor (n = 1.34), it experiences refraction. The refraction occurs at the surface of the cornea due to the change in the refractive index. The lens formula
`\( (1)/(f) = (1)/(d_o) + (1)/(d_i) \)` describes the relationship between object distance (\(d_o\)), image distance
`(\(d_i\))` , and focal length
`(\(f\))` .

For the cornea, assuming the image distance is represented by
`\(d_i\)` and the object distance is
`\(d_o = -9.30 \, \text{cm}\)` (as the object is placed in front of the cornea), the refractive index of air
`(\(n \approx 1\))` remains negligible. Therefore, using the lens formula and given the thinness of the cornea, the image distance
`\(d_i\)` can be calculated.

`\[ (1)/(f) = (1)/(d_o) + (1)/(d_i) \]`

`\[ \text{Given} \, d_o = -9.30 \, \text{cm}, \, n = 1.34 \, \text{(refractive index of aqueous humor)} \]`

Solving for
`\(d_i\)` yields the image distance formed by the cornea alone, which is approximately 0.0933 cm. This calculation assumes a thin lens approximation and ignores complexities like the thickness of the cornea, but it provides a basic estimation of the image distance formed by the cornea in this scenario.