Solving MCAT Questions: Lens Adjustments and Index of Refraction Explained

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SUMMARY

This discussion addresses two MCAT-related physics questions involving lens adjustments and the index of refraction. The first question requires the application of the lens formula 1/o + 1/i = 1/f to determine the radius of curvature and power of a contact lens, despite confusion over the applicability of 1/f = 2/r. The second question involves calculating the index of refraction of glass when a beam of monochromatic light strikes it at a 60-degree angle, with the reflected and refracted beams being perpendicular. Key insights include the importance of visualizing the scenario through diagrams and recognizing that the index of refraction for the lens is necessary for accurate calculations.

PREREQUISITES
  • Understanding of the lens formula: 1/o + 1/i = 1/f
  • Knowledge of the relationship between focal length and radius of curvature for lenses
  • Familiarity with the concept of index of refraction
  • Ability to visualize and draw ray diagrams for light behavior at interfaces
NEXT STEPS
  • Study the derivation and applications of the lens formula in optics
  • Learn about the calculation of lens power and its relation to curvature
  • Explore Snell's Law and its implications for calculating the index of refraction
  • Practice drawing ray diagrams for various optical scenarios
USEFUL FOR

Students preparing for the MCAT, physics educators, and anyone interested in mastering optics concepts related to lenses and light behavior.

derbu
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First question: The near point, or neatest point at which an object can be seen clearly, for one of your eye is 100cm. You wish to see your friend's face clearly when she stands 50cm in front of you. If you use a tact lens to adjust your eyesight, what must be the radius of curvature and power of the contact lens.

I understand that you have to use the 1/o + 1/i = 1/f equation but, I was told 1/f =2/r is only for mirrors and does not apply to lenses. If 1/f = 2/r can't be used, I don't know any way of solving it.

Second question: Imagine that a beam of monochromatic light originates in air and is allowed to shine upon the flat surface of a piece of glass at an able of 60 degree with the horizontal. THe reflected and refracted beams are perpendicular to each other What is the index of refraction of the glass?

I just can't seem to draw a diagram that makes sense for this question, if someone could explain in detail, that would help a lot!

Thanks in advance!

 
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The first question is ridiculous. You're not given the index of refraction for the lens. I guess use 1/f=2/r, implying an index of 2.

For the second question it may help your visualization if you draw the piece of glass vertically on your paper, and orient the beam respectively.
 
thanks! makes sense now for the second question
 

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