A small pin fixed on a tabletop 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? The refractive index of glass=1.5.Does the answer depend on the location of the slab?
A small pin fixed on a tabletop 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? The refractive index of glass=1.5.Does the answer depend on the location of the slab?
Solution and Explanation
Actual depth of the pin,d=15cm
The apparent depth of the pin=d'
The refractive index of glass,\(\mu\)=1.5
The ratio of actual depth to apparent depth is equal to the refractive index of glass,i.e.,\(\mu\)=\(\frac{d}{d'}\)
∴d'=\(\frac{d}{\mu}\)=\(\frac{15}{1.5}\)=10cm
The distance at which the pin appears to be raised=d'-d=15-10=5cm
For a small angle of incidence, this distance does not depend upon the location of the slab.
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Concepts Used:
Ray Optics and Optical Instruments
Optics, deals with the determination of behaviour and the properties of light, along with its interactions with the matter and also with the instruments that are used to detect it.
Ray optics is also known as the geometrical optics and it is a branch of science which describes light propagation.
Reflection is the change in direction of light at an interface in-between two different media so that the wave-front returns into a medium from which it was originated.
Speed of light is the rate at which the light travels in free space.
A phenomenal change in image formed when the light is passed from one medium to another which is called Refraction.
Total Internal Reflection is the reflection of light when the light ray enters into a rarer medium from a denser medium and the angle of incidence is higher than the critical angle of incidence then that light ray will be reflected back to the denser medium.
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