Answer
437.1k+ views
Hint: To calculate the net dispersion, calculate the dispersion due to each prism, by taking the average of the refractive indices. Since there is no deviation, we can equate the deviation of the combination to $0$.
Formula used:
$\delta=\delta_{c}+\delta_{f}$
$\delta=(\mu-1)A$
Complete step by step answer:
Given that, for crown glass,
Refractive index for blue light: $\mu_{b}=1.51$
Refractive index for red light: $\mu_{r}=1.49.$
Angle $A_{c}=6^{\circ}$
For flint,
Refractive index for blue light: $\mu_{b}\prime=1.77$
Refractive index for red light: $\mu_{r}\prime=1.73$
Angle $A_{f}=x$
For combination of prisms, net deviation is given by $\delta=\delta_{c}+\delta_{f}$, where $\delta_{c}$ is the deviation due to crown prism and $\delta_{f}$ is the deviation due to flint prism.
For no deviation $\delta=\delta_{c}+\delta_{f}=0$
$\delta_{c}=-\delta_{f}$
We also know that $\delta=(\mu-1)A$ where $\mu$ is the average refractive index
Then, $\mu=\dfrac{\mu_{b}+\mu_{r}}{2}=\dfrac{1.51+1.49}{2}=1.50$
Similarly, $\mu\prime=\dfrac{\mu_{b}\prime+\mu_{r}\prime}{2}=\dfrac{1.77+1.73}{2}=1.75$
Then from $\delta_{c}=-\delta_{f}$
$(\mu-1)A_{c}=-(\mu\prime-1)A_{f}$
$(1.50-1)\times 6=-(1.75-1)\times x$
$x=-\dfrac{0.5\times 6}{0.75}$
$x=-4^{\circ}$
Hence, the net dispersion angle of the flint is $4^{\circ}$.
Note:
The negative sign implies that the combination must be another way. i.e. the flint followed by the crown prism. Only since there is no deviation, we equate the net deviation to $0$, which reduces the problem to a simple ratio.
Formula used:
$\delta=\delta_{c}+\delta_{f}$
$\delta=(\mu-1)A$
Complete step by step answer:
Given that, for crown glass,
Refractive index for blue light: $\mu_{b}=1.51$
Refractive index for red light: $\mu_{r}=1.49.$
Angle $A_{c}=6^{\circ}$
For flint,
Refractive index for blue light: $\mu_{b}\prime=1.77$
Refractive index for red light: $\mu_{r}\prime=1.73$
Angle $A_{f}=x$
For combination of prisms, net deviation is given by $\delta=\delta_{c}+\delta_{f}$, where $\delta_{c}$ is the deviation due to crown prism and $\delta_{f}$ is the deviation due to flint prism.
![seo images](https://www.vedantu.com/question-sets/aa2b0dc9-a188-411e-9544-a862f5373b6a4608221680894259017.png)
For no deviation $\delta=\delta_{c}+\delta_{f}=0$
$\delta_{c}=-\delta_{f}$
We also know that $\delta=(\mu-1)A$ where $\mu$ is the average refractive index
Then, $\mu=\dfrac{\mu_{b}+\mu_{r}}{2}=\dfrac{1.51+1.49}{2}=1.50$
Similarly, $\mu\prime=\dfrac{\mu_{b}\prime+\mu_{r}\prime}{2}=\dfrac{1.77+1.73}{2}=1.75$
Then from $\delta_{c}=-\delta_{f}$
$(\mu-1)A_{c}=-(\mu\prime-1)A_{f}$
$(1.50-1)\times 6=-(1.75-1)\times x$
$x=-\dfrac{0.5\times 6}{0.75}$
$x=-4^{\circ}$
Hence, the net dispersion angle of the flint is $4^{\circ}$.
Note:
The negative sign implies that the combination must be another way. i.e. the flint followed by the crown prism. Only since there is no deviation, we equate the net deviation to $0$, which reduces the problem to a simple ratio.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)