A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30 cm and refractive index 1.5. The distance from the centre of the globe at which the beam of light can converge is________ mm.
Correct Answer: 225
Solution and Explanation
The correct answer is: 225
1st refraction:
\(\frac{1.5}{V_1}-0=\frac{0.5}{15}\)
\(⇒ v_1 = 45 \)cm
2nd refraction:
\(\frac{1}{v_2}-\frac{1.5}{15}=\frac{-0.5}{-15}\)
\(⇒ \frac{1}{v_2}=\frac{1}{30}+\frac{1}{10}\)
\(⇒ v2 = +7.5 \)cm
\(⇒\) Distance from centre = 22.5 cm
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Concepts Used:
Types of Differential Equations
There are various types of Differential Equation, such as:
Ordinary Differential Equations:
Ordinary Differential Equations is an equation that indicates the relation of having one independent variable x, and one dependent variable y, along with some of its other derivatives.
\(F(\frac{dy}{dt},y,t) = 0\)
Partial Differential Equations:
A partial differential equation is a type, in which the equation carries many unknown variables with their partial derivatives.
Linear Differential Equations:
It is the linear polynomial equation in which derivatives of different variables exist. Linear Partial Differential Equation derivatives are partial and function is dependent on the variable.
Homogeneous Differential Equations:
When the degree of f(x,y) and g(x,y) is the same, it is known to be a homogeneous differential equation.
\(\frac{dy}{dx} = \frac{a_1x + b_1y + c_1}{a_2x + b_2y + c_2}\)
Read More: Differential Equations