Question

A child notices that he is having a tough time seeing the whiteboard so he decides to see the doctor to get his eyes checked. The doctor tells the child that he has Myopia and has a far sight of 81cm.

1. Does the child need planoconvex or planoconcave glasses?

The index of refraction of the glasses are 1.57 and they also have a thin coating of antireflective material on the outside of the glasses.   Assume the boy wears the glasses 2cm away from his eye. The index of refraction of the coating is 1.68.

2. If the curved side of the glasses is toward the eye, what is its radius of curvature?  
3. What is the minimum thickness of the coating so that it can be most effective at 570nm?                         

Answer 1

A. As the boy as myopia, it is corrected by planoconcave lens. in myopia, the eyeball is enlarged and the image does not fall on the retina and hence, a diverging/ concave lens will help to form the image on the retina.

GIVEN: far sight, image distance, v = 81 cm

The index of refraction of the glasses , n= 1.57

The index of refraction of the coating is 1.68.

A. radius of curvature of a plano concave lens,

Radius, r = f * (n-1)

the focal length,f is calculated by, (1/f) = (1/u) + (1/v) = (1/infinity) + (1/81) = 0 + 1/81

=> f = 81 cm

=> radius of curvatute, r = 81 *(1.57-1) = 46.17 cm

B. the minimum thickness of the coating so that it can be most effective at 570nm

for an effective viewing, the minimum thickness is given by,

t = (wavelength of light) / (4* refractive index of coating) = 570 / (4*1.68) = 84.82 nm