Physics-
General
Easy
Question
Following figure shows the multiple reflections of a light ray along a glass corridor where the walls are either parallel or perpendicular to one another. If the angle of incidence at point P is 30°, what are the angles of reflection of the light ray at points Q, R, S and T respectively
![](data:image/png;base64,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)
The correct answer is: ![30 to the power of ring operator end exponent comma 60 to the power of ring operator end exponent comma 60 to the power of ring operator end exponent comma 30 to the power of ring operator end exponent](data:image/png;base64,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)
Related Questions to study
physics-
Which of the following ray diagram show physically possible refraction
![](data:image/png;base64,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)
Which of the following ray diagram show physically possible refraction
![](data:image/png;base64,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)
physics-General
physics-
A water drop in air refractes the light ray as
A water drop in air refractes the light ray as
physics-General
physics-
A small fish 0.4 m below the surface of a lake, is viewed through a simple converging lens of focal length 3 m. The lens is kept at 0.2 m above the water surface such that fish lies on the optical axis of the lens. The image of the fish seen by observer will be at ![open parentheses mu subscript w a t e r end subscript equals fraction numerator 4 over denominator 3 end fraction close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
A small fish 0.4 m below the surface of a lake, is viewed through a simple converging lens of focal length 3 m. The lens is kept at 0.2 m above the water surface such that fish lies on the optical axis of the lens. The image of the fish seen by observer will be at ![open parentheses mu subscript w a t e r end subscript equals fraction numerator 4 over denominator 3 end fraction close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
physics-
In a thin spherical fish bowl of radius 10 cm filled with water of refractive index 4/3 there is a small fish at a distance of 4 cm from the centre C as shown in figure. Where will the image of fish appears, if seen from E
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)
In a thin spherical fish bowl of radius 10 cm filled with water of refractive index 4/3 there is a small fish at a distance of 4 cm from the centre C as shown in figure. Where will the image of fish appears, if seen from E
![](data:image/png;base64,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)
physics-General
physics-
An object is placed at a point distant x from the focus of a convex lens and its image is formed at I as shown in the figure. The distances x, x' satisfy the relation
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)
An object is placed at a point distant x from the focus of a convex lens and its image is formed at I as shown in the figure. The distances x, x' satisfy the relation
![](data:image/png;base64,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)
physics-General
physics-
Three lenses
are placed co-axially as shown in figure. Focal length's of lenses are given 30 cm, 10 cm and 5 cm respectively. If a parallel beam of light falling on lens
, emerging
as a convergent beam such that it converges at the focus of
. Distance between
and
will be
![](data:image/png;base64,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)
Three lenses
are placed co-axially as shown in figure. Focal length's of lenses are given 30 cm, 10 cm and 5 cm respectively. If a parallel beam of light falling on lens
, emerging
as a convergent beam such that it converges at the focus of
. Distance between
and
will be
![](data:image/png;base64,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)
physics-General
physics-
for a gas is 5/3 An ideal gas at
is compressed adiabatically to 8/27 of its original volume The rise in temperature of the gas is
for a gas is 5/3 An ideal gas at
is compressed adiabatically to 8/27 of its original volume The rise in temperature of the gas is
physics-General
physics-
A wire is stretched by 0.01 m by a certain force F Another wire of same material whose diameter and length are double to the original wire is stretched by the same force ? Then what will be its. elongation?
A wire is stretched by 0.01 m by a certain force F Another wire of same material whose diameter and length are double to the original wire is stretched by the same force ? Then what will be its. elongation?
physics-General
physics-
To keep constant time, watches are fitted with balance wheel made of.....
To keep constant time, watches are fitted with balance wheel made of.....
physics-General
physics-
Consider the melting of 1g of ice at
to water at
at atmospheric pressure Then the change in internal energy of the system(density of ice is 920kg/m3
Consider the melting of 1g of ice at
to water at
at atmospheric pressure Then the change in internal energy of the system(density of ice is 920kg/m3
physics-General
maths-
The mean and variance of the random variable X which follows the following distribution are respectively ![](data:image/png;base64,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)
The mean and variance of the random variable X which follows the following distribution are respectively ![](data:image/png;base64,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)
maths-General
maths-
If X is a random variable with the following distribution
where p+q=1 then the variance of X is
If X is a random variable with the following distribution
where p+q=1 then the variance of X is
maths-General
physics-
On applying a stress of
the length of a perfect elastic wire is doubled. What will be its Young's modulus?
On applying a stress of
the length of a perfect elastic wire is doubled. What will be its Young's modulus?
physics-General
physics-
A fixed volume of iron is drawn into a wire of length L. The extension X produced in this wire be a constant force F is proportional to…….
A fixed volume of iron is drawn into a wire of length L. The extension X produced in this wire be a constant force F is proportional to…….
physics-General
physics-
A wire of diameter 1 mm breaks under a tension of 100 N. Another wire of same material as that of the first one, but of diameter 2 mm breaks under a tension of……..
A wire of diameter 1 mm breaks under a tension of 100 N. Another wire of same material as that of the first one, but of diameter 2 mm breaks under a tension of……..
physics-General