Math Is Fun Forum
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#1 2014-03-30 14:27:25
Optics
3. A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index of water? If water is replaced by a liquid of refractive index 1.63 cm upto the same height, by what distance would the microscope have to be moved to focus on the needle again?
4. A convex lens of focal length 10 cm is placed coaxially 5 cm away from a concave lend of focal length 10 cm, if an object is placed 30 cm in front of convex lens find the position of the final image formed by the combined system.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
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#2 2014-03-30 23:29:12
- ShivamS
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- Registered: 2011-02-07
- Posts: 3,648
Re: Optics
3. 1.73 cm
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#3 2014-03-31 01:05:51
Re: Optics
Explanation please.
Can you do four? (you sure can)
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#4 2014-03-31 08:20:18
- ShivamS
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- Registered: 2011-02-07
- Posts: 3,648
Re: Optics
3. Let a and b represent the actual and apparent depth of the needle respectively.
a = 12.5 cm
b = 9.4 cm
Now we need the index of refraction of water. I am presuming you haven't been told the speed of light in water, so we need to find it. Note that the index of refraction is also equal to actual depth/apparent depth.
Index of refraction of water = 12.5/9.4 = 1.33 approximately
The liquid by which water is replaced has an index of refraction of 1.63 and therefore the apparent depth changes (obviously the actual depth remains the same). Let c represent the new apparent depth.
As before, actual depth/apparent depth = index of refraction.
1.63=12.5/c Solving gives us c = 7.67 cm approximately
Now the apparent depth is approximately 1.73 cm higher then before so the microscope must be moved up 1.73 cm.
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#5 2014-04-01 01:20:49
Re: Optics
actual depth/apparent depth = index of refraction
Thanks, I needed that.
Will you please help me with 4?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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