Solving MCAT Questions: Lens Adjustments and Index of Refraction Explained

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To solve the first MCAT question regarding contact lenses, the equation 1/o + 1/i = 1/f is essential, but the radius of curvature and power cannot be determined without knowing the index of refraction of the lens material. The second question involves a beam of light striking glass at a 60-degree angle, where the reflected and refracted beams are perpendicular, indicating a specific relationship that can help find the index of refraction. Visualizing the setup with a diagram can clarify the angles and relationships involved in the second question. The discussion highlights the importance of understanding lens formulas and the need for additional information to solve optical problems effectively. Overall, both questions emphasize the application of optics principles in practical scenarios.
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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
 
Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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