Question
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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)
- 5.2 cm
- 7.2 cm
- 4.2 cm
- 3.2 cm
The correct answer is: 5.2 cm
By using ![fraction numerator mu subscript 2 end subscript over denominator v end fraction minus fraction numerator mu subscript 1 end subscript over denominator u end fraction equals fraction numerator mu subscript 2 end subscript minus mu subscript 1 end subscript over denominator R end fraction](data:image/png;base64,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)
where
v = ?
On putting values ![v equals negative 5.2 c m](data:image/png;base64,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)
Related Questions to study
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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)
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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)
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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)
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
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?
To keep constant time, watches are fitted with balance wheel made of.....
To keep constant time, watches are fitted with balance wheel made of.....
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
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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)
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
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?
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…….
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……..
A steel ring of radius r and cross-section area ' A ' is fitted on to a wooden dise of radius
If young's modulus be E then what is force with which the steel nine is expanded ?
A steel ring of radius r and cross-section area ' A ' is fitted on to a wooden dise of radius
If young's modulus be E then what is force with which the steel nine is expanded ?
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means