Physics
General
Easy

Question

A vessels of depth t is half filled with oil of refractive index n subscript 1 and the other half is filled with water (refractive index n subscript 2 ). The apparent depth of the vessel when viewed from above is…….

  1. fraction numerator 2 t left parenthesis n subscript 1 minus end subscript n subscript 2 right parenthesis end subscript right parenthesis over denominator n subscript 1 space end subscript n subscript 2 end fraction
  2. fraction numerator 2 t open parentheses n subscript 1 plus n subscript 2 close parentheses over denominator n subscript 1 n subscript 2 end fraction
  3. fraction numerator t open parentheses n subscript 1 minus n subscript 2 close parentheses over denominator 2 n subscript 1 n subscript 2 end fraction
  4. fraction numerator t open parentheses n subscript 1 plus n subscript 2 close over denominator 2 n subscript 1 n subscript 2 end fraction

The correct answer is: fraction numerator t open parentheses n subscript 1 plus n subscript 2 close over denominator 2 n subscript 1 n subscript 2 end fraction

Related Questions to study

General
physics

A plane mirror is placed at the bottom of a tank containing a liquid of refractive index n.P.  is a small object at a height h above the mirror. An observer 0, vertically above  P, outside the liquid sees P and its image in the mirror. The apparent distance between these two wall be.

A plane mirror is placed at the bottom of a tank containing a liquid of refractive index n.P.  is a small object at a height h above the mirror. An observer 0, vertically above  P, outside the liquid sees P and its image in the mirror. The apparent distance between these two wall be.

physicsGeneral
General
Maths-

The length of the normal to the curve y equals a c o s space h open parentheses x over a close parentheses at any point varies as

The given curve is y equals a cos h open parentheses x over a close parentheses
Ordinate means the y-axis
And abscissa means x-axis
The formula of length of the normal at point (x,y) is given by L e n g t h space equals space open vertical bar y subscript 1 square root of 1 space plus space m end root close vertical bar

Here, m = open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript left parenthesis x subscript 1 comma y subscript 1 right parenthesis end subscript
Now, we will find the value of fraction numerator d y over denominator d x end fraction
y equals a cos h open parentheses x over a close parentheses
fraction numerator d y over denominator d x end fraction equals a sin h open parentheses x over a close parentheses fraction numerator d over denominator d x end fraction open parentheses x over a close parentheses space space space space space space space space space space space space space space space space space... left curly bracket fraction numerator d over denominator d x end fraction cos h x space equals space minus sin h x right curly bracket
space space space space space space space equals space minus a sin h open parentheses x over a close parentheses space cross times 1 over a
space space space space space space space equals negative sin h open parentheses x over a close parentheses
 m space equals open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript left parenthesis x subscript 1 comma y subscript 1 right parenthesis end subscript
space space space space equals negative sin h open parentheses x subscript 1 over a close parentheses
We will substitute this value in the formula of length.
L e n g t h equals vertical line y subscript 1 square root of 1 plus m squared end root vertical line
space space space space space space space space space space space space space equals vertical line y subscript 1 square root of 1 space plus space left parenthesis negative sin h x over a end root right parenthesis squared vertical line
space space space space space space space space space space space space space equals vertical line y subscript 1 square root of cos h squared x over a end root vertical line space space space space space space space space space space space space space space... left curly bracket 1 space plus space sin h squared x space equals space cos h squared x right parenthesis
space space space space space space space space space space space space space equals open vertical bar y subscript 1 cos h x over a close vertical bar
space space y subscript 1 space end subscript equals space a cos h x over a
s o comma space cos h x over a equals y subscript 1 over a
L e n g t h space equals space vertical line y subscript 1 cross times y subscript 1 over a vertical line
space space space space space space space space space space space space space space equals y subscript 1 squared over a
Length is proportional to y12 as "a" is constant.
We can see the length of the normal depends on the square of y. It means the length of normal varies square of ordinate.

The length of the normal to the curve y equals a c o s space h open parentheses x over a close parentheses at any point varies as

Maths-General
The given curve is y equals a cos h open parentheses x over a close parentheses
Ordinate means the y-axis
And abscissa means x-axis
The formula of length of the normal at point (x,y) is given by L e n g t h space equals space open vertical bar y subscript 1 square root of 1 space plus space m end root close vertical bar

Here, m = open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript left parenthesis x subscript 1 comma y subscript 1 right parenthesis end subscript
Now, we will find the value of fraction numerator d y over denominator d x end fraction
y equals a cos h open parentheses x over a close parentheses
fraction numerator d y over denominator d x end fraction equals a sin h open parentheses x over a close parentheses fraction numerator d over denominator d x end fraction open parentheses x over a close parentheses space space space space space space space space space space space space space space space space space... left curly bracket fraction numerator d over denominator d x end fraction cos h x space equals space minus sin h x right curly bracket
space space space space space space space equals space minus a sin h open parentheses x over a close parentheses space cross times 1 over a
space space space space space space space equals negative sin h open parentheses x over a close parentheses
 m space equals open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript left parenthesis x subscript 1 comma y subscript 1 right parenthesis end subscript
space space space space equals negative sin h open parentheses x subscript 1 over a close parentheses
We will substitute this value in the formula of length.
L e n g t h equals vertical line y subscript 1 square root of 1 plus m squared end root vertical line
space space space space space space space space space space space space space equals vertical line y subscript 1 square root of 1 space plus space left parenthesis negative sin h x over a end root right parenthesis squared vertical line
space space space space space space space space space space space space space equals vertical line y subscript 1 square root of cos h squared x over a end root vertical line space space space space space space space space space space space space space space... left curly bracket 1 space plus space sin h squared x space equals space cos h squared x right parenthesis
space space space space space space space space space space space space space equals open vertical bar y subscript 1 cos h x over a close vertical bar
space space y subscript 1 space end subscript equals space a cos h x over a
s o comma space cos h x over a equals y subscript 1 over a
L e n g t h space equals space vertical line y subscript 1 cross times y subscript 1 over a vertical line
space space space space space space space space space space space space space space equals y subscript 1 squared over a
Length is proportional to y12 as "a" is constant.
We can see the length of the normal depends on the square of y. It means the length of normal varies square of ordinate.
General
physics

A ray of light is incident on one  equilateral glass prism placed on a horizontal table. For minimum deviation which of the following is true?

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A ray of light is incident normally on one of the faces of a proms of apex 30 to the power of 0  and  n=square root of 2 what is the angle of deeviation which of the following is true?

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There is a prism with refractive index equal to square root of 2 and the refracting angle equal to 30 to the power of 0. One of the refracting surfaces of the prism is polished. A beam of monochromatic light will retrace its path if its angle of incidence over the refracting surface of the prism is.........

There is a prism with refractive index equal to square root of 2 and the refracting angle equal to 30 to the power of 0. One of the refracting surfaces of the prism is polished. A beam of monochromatic light will retrace its path if its angle of incidence over the refracting surface of the prism is.........

physicsGeneral
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The minimum angle of deviation of a prism of refractive index 1.732  is equal to its refracting angle. What is the angle of prism?

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An equilateral prism deviates a ray through 45 to the power of 0 for two angles of incidence differing by 20 to the power of 0 . What is the nof the prism?

An equilateral prism deviates a ray through 45 to the power of 0 for two angles of incidence differing by 20 to the power of 0 . What is the nof the prism?

physicsGeneral
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The minimum deviation produced by a glass prism of angle 60 to the power of 0  is  30 to the power of 0. If the velocity of light in vaccum is 3 cross times 10 to the power of 8 space end exponent m divided by s. Then what is the velocity of light in glass in m/s ?

The minimum deviation produced by a glass prism of angle 60 to the power of 0  is  30 to the power of 0. If the velocity of light in vaccum is 3 cross times 10 to the power of 8 space end exponent m divided by s. Then what is the velocity of light in glass in m/s ?

physicsGeneral
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Two identical parallel plate capacitors are placed in series and connected to a constant voltage source of V volt. If one of the capacitor is completely immersed in a liquid of dielectric constant K, then the potential difference between the plates of the other capacitor will change to

In series combination, charge is constant.
therefore blank V proportional to fraction numerator 1 over denominator C end fraction
Now, fraction numerator V subscript 2 end subscript over denominator V subscript 1 end subscript end fraction equals fraction numerator K C over denominator C end fraction equals fraction numerator K over denominator 1 end fraction
But V subscript 1 end subscript plus V subscript 2 end subscript blank equals V
or fraction numerator V subscript 2 end subscript over denominator K end fraction plus V subscript 2 end subscript blank equals V blank o r blank V subscript 2 end subscript equals fraction numerator K over denominator K plus 1 end fraction V

Two identical parallel plate capacitors are placed in series and connected to a constant voltage source of V volt. If one of the capacitor is completely immersed in a liquid of dielectric constant K, then the potential difference between the plates of the other capacitor will change to

physics-General
In series combination, charge is constant.
therefore blank V proportional to fraction numerator 1 over denominator C end fraction
Now, fraction numerator V subscript 2 end subscript over denominator V subscript 1 end subscript end fraction equals fraction numerator K C over denominator C end fraction equals fraction numerator K over denominator 1 end fraction
But V subscript 1 end subscript plus V subscript 2 end subscript blank equals V
or fraction numerator V subscript 2 end subscript over denominator K end fraction plus V subscript 2 end subscript blank equals V blank o r blank V subscript 2 end subscript equals fraction numerator K over denominator K plus 1 end fraction V
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A light ray is incident perpendicular to one face of  90 to the power of 0 prism and is totally internally reflected at the glass-air interface. If the angle of reflection is  45 to the power of 0. We conclude that the refractive index....
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A ray falls on a prism  ABC(AB=BC) and travels as shown in the figure. The minimum refractive, index of the prism material should be.

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Two  parallel light rays are incident at one surface of a prism of refractive index  as shown in figure. What is the angle between the rays as they emerge ?

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An object is placed at a distance of f over 2 the from a convex lens the image will be ...

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