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A small pin fixed on a table top is viewed from above from a distance of 50cm. By what distance would the pin appear to be raised if it is viewed from the same point through a 15cm thick glass slab held parallel to the table? Refractive index of glass = 1.5. Does the answer depend on the location of the slab?
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1. Given Data
- Real thickness of slab (t): 15 cm
- Refractive index of glass (n): 1.5
2. Calculating the Normal Shift
The apparent rise (normal shift) produced by a glass slab is given by the formula:
Shift = t × (1 - 1/n)
Substituting the values:
- Shift = 15 × (1 - 1/1.5)
- Shift = 15 × (1 - 10/15)
- Shift = 15 × (1 - 2/3)
- Shift = 15 × (1/3)
- Shift = 5 cm
Apparent Rise (Shift) = 5 cm
3. Does it depend on the slab's location?
No. The answer does not depend on the location of the slab.
The apparent shift is determined solely by the thickness of the slab (t) and its refractive index (n). As long as the slab is placed anywhere between the object (pin) and the observer, the shift will remain exactly 5 cm.
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