Ray optics: A rectangular glass and a convex lens, then find the index of refraction of the glass
Question: A rectangular glass, a convex lens, and a screen are placed as shown in the figure. A 2.0-cm-high object, […]
Equation related to limit: Find the parameters
Question: If the following equation holds, \[ \lim_{x \rightarrow 2}\frac{\sqrt{9+ax}+b}{x-2}=-2 \] Find parameters, \(a\) and \(b\). Answer: Since the extreme […]
Potential energy created by one-dimensional infinite numbers of charges
Question: Infinite numbers of positive and singly negative charged ions are placed in a straight line alternatively with spacing of […]
Use Young’s double slit to find laser’s wavelength
Question: There is a double slit whose separation distance of slits is 0.100 mm. The distance from the slit to […]
How do we find the figure of some of big number?
Question: Knowing that \(\log_{10}2=0.3010\) and \(\log_{10}3=0.4771\), (1) find the number of figures of \(6^{50}\). (2) find at which decimal place […]
Finding the capacitance of a parallel plate capacitor with two different dielectric constants
Question: There is a parallel plate capacitor the area of \(L^2\) and separation distance of \(d\). A half of the […]
De Moivre’s theorem and its application
Question: By using De Moivre’s theorem, simplify the following expressions: (1) \(\left(\frac{1+\sqrt{3}i}{2}\right)^{10}\) (2) \(\left(\frac{\sqrt{3}+i}{1+i}\right)^{6}\) Answer: De Moivre’s theorem reads \[ […]
Dropping a coin to find out the depth of a well
Question: You released a coin in order to find the depth of a well. The time between dropping the coin […]
Static equilibrium of forces
Question: When this system is at equilibrium, find the tension in cord b, \(T_b\), knowing that the hanging mass is […]
Find the extrema: an optimization problem with Lagrange multipliers
Question: By using Lagrange multipliers, find the extrema of \(x^2+2y^2+3z^2\) when \(3x+2y+z=-1\). Answer: This is the exactly the same question […]