
A transparent (glass) sphere has a small, opaque dot at its centre. Does the apparent position of a dot appear to be the same as its actual position when observed from outside?
Answer
488.7k+ views
Hint: According to Snell’s law the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant. All the rays that come out from an object that is kept at the centre of a transparent sphere will be normal to the surface of the sphere. The light will be reflected inside the sphere.
Complete step by step answer:
When light falls normally on the boundary surface then the angle if incidence will be $0$,
We will apply the lens formula considering the refractive indices of the medium involved
According to this formula;
$\dfrac{{{\mu _2}}}{v} - \dfrac{{{\mu _1}}}{u} = \dfrac{{\left( {{\mu _2} - {\mu _1}} \right)}}{R}$ ……………………………………… (i)
As we know that refractive index of glass is will be constant ${\mu _1} = \mu $,
${\mu _2}$(refractive index of surrounding) will be 1, $u = - R$ = {Radius of sphere} and \[R = - R\] is the radius of sphere
Substituting these values in equation (i)
We get,
$\dfrac{1}{v} - \dfrac{\mu }{{ - R}} = \dfrac{{\left( {1 - \mu } \right)}}{{ - R}}$………………………………………………(ii)
On solving above equation, we get,
$\dfrac{1}{v} = \dfrac{1}{{ - R}}$ …………………………………………………………….(iii)
From above relation, we can say that the "there will be no change in the position of an opaque dot at the centre of a transparent glass sphere when a person observes it from the outside."
Note:
When light falls normally on the boundary surface, then we have angle of incidence $i = 0$ and
According to Snell's law \[{\mu _1}\sin i\; = {\mu _2}\sin r.\] So, there will be no refraction, i.e. r is also zero. Thus, the light will be totally internally reflected.
Hence the object will be observed at the same position from outside, and this and will be independent of the refractive index of the sphere
Complete step by step answer:
When light falls normally on the boundary surface then the angle if incidence will be $0$,
We will apply the lens formula considering the refractive indices of the medium involved
According to this formula;
$\dfrac{{{\mu _2}}}{v} - \dfrac{{{\mu _1}}}{u} = \dfrac{{\left( {{\mu _2} - {\mu _1}} \right)}}{R}$ ……………………………………… (i)
As we know that refractive index of glass is will be constant ${\mu _1} = \mu $,
${\mu _2}$(refractive index of surrounding) will be 1, $u = - R$ = {Radius of sphere} and \[R = - R\] is the radius of sphere
Substituting these values in equation (i)
We get,
$\dfrac{1}{v} - \dfrac{\mu }{{ - R}} = \dfrac{{\left( {1 - \mu } \right)}}{{ - R}}$………………………………………………(ii)
On solving above equation, we get,
$\dfrac{1}{v} = \dfrac{1}{{ - R}}$ …………………………………………………………….(iii)
From above relation, we can say that the "there will be no change in the position of an opaque dot at the centre of a transparent glass sphere when a person observes it from the outside."
Note:
When light falls normally on the boundary surface, then we have angle of incidence $i = 0$ and
According to Snell's law \[{\mu _1}\sin i\; = {\mu _2}\sin r.\] So, there will be no refraction, i.e. r is also zero. Thus, the light will be totally internally reflected.
Hence the object will be observed at the same position from outside, and this and will be independent of the refractive index of the sphere
Recently Updated Pages
Express the following as a fraction and simplify a class 7 maths CBSE

The length and width of a rectangle are in ratio of class 7 maths CBSE

The ratio of the income to the expenditure of a family class 7 maths CBSE

How do you write 025 million in scientific notatio class 7 maths CBSE

How do you convert 295 meters per second to kilometers class 7 maths CBSE

Write the following in Roman numerals 25819 class 7 maths CBSE

Trending doubts
Give 10 examples of unisexual and bisexual flowers

Draw a labelled sketch of the human eye class 12 physics CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Differentiate between insitu conservation and exsitu class 12 biology CBSE

What are the major means of transport Explain each class 12 social science CBSE

Franz thinks Will they make them sing in German even class 12 english CBSE
