Explanation:
It is given that,
Refractive index of zircon, n = 1.923
The wavelength of visible light ranging from 380 nm to 760 nm in a vacuum.
Wavelength 1, ![\lambda_1=380\ nm=380\times 10^{-9}\ m](https://tex.z-dn.net/?f=%5Clambda_1%3D380%5C%20nm%3D380%5Ctimes%2010%5E%7B-9%7D%5C%20m)
Wavelength 2, ![\lambda_2=760\ nm=760\times 10^{-9}\ m](https://tex.z-dn.net/?f=%5Clambda_2%3D760%5C%20nm%3D760%5Ctimes%2010%5E%7B-9%7D%5C%20m)
We need to find the shortest and longest wavelength. For shortest wavelength, ![\lambda_s=\dfrac{\lambda_1}{n}](https://tex.z-dn.net/?f=%5Clambda_s%3D%5Cdfrac%7B%5Clambda_1%7D%7Bn%7D)
![\lambda_s=\dfrac{380\times 10^{-9}}{1.923}=1.97\times 10^{-7}\ m](https://tex.z-dn.net/?f=%5Clambda_s%3D%5Cdfrac%7B380%5Ctimes%2010%5E%7B-9%7D%7D%7B1.923%7D%3D1.97%5Ctimes%2010%5E%7B-7%7D%5C%20m)
For longest wavelength, ![\lambda_l=\dfrac{\lambda_2}{n}](https://tex.z-dn.net/?f=%5Clambda_l%3D%5Cdfrac%7B%5Clambda_2%7D%7Bn%7D)
![\lambda_l=\dfrac{760\times 10^{-9}}{1.923}=3.95\times 10^{-7}\ m](https://tex.z-dn.net/?f=%5Clambda_l%3D%5Cdfrac%7B760%5Ctimes%2010%5E%7B-9%7D%7D%7B1.923%7D%3D3.95%5Ctimes%2010%5E%7B-7%7D%5C%20m)
Hence, this is the required solution.
<span>Mineral is an inorganic solid, characterized with a definite chemical composition and ordered internal structure.</span>
Both plastic and concrete are not minerals because they are made by humans. They are not naturally occurring materials, which the minerals are.
Explanation:
For Gain of −10
Inverting op-amp gain is given by
![Gain=V_{out} /V_{in} = -R_{f} /R_{in}](https://tex.z-dn.net/?f=Gain%3DV_%7Bout%7D%20%2FV_%7Bin%7D%20%3D%20-R_%7Bf%7D%20%2FR_%7Bin%7D)
The negative sign represents output signal being phase shifted by 180°
![-10=-10/R_{in}](https://tex.z-dn.net/?f=-10%3D-10%2FR_%7Bin%7D)
![R_{in} =-10k/-10](https://tex.z-dn.net/?f=R_%7Bin%7D%20%3D-10k%2F-10)
Ω
For Gain of −1
![Gain= -R_{f} /R_{in}](https://tex.z-dn.net/?f=Gain%3D%20-R_%7Bf%7D%20%2FR_%7Bin%7D)
![-1=-10k/R_{in}](https://tex.z-dn.net/?f=-1%3D-10k%2FR_%7Bin%7D)
![R_{in} =-10k/-1](https://tex.z-dn.net/?f=R_%7Bin%7D%20%3D-10k%2F-1)
Ω
For Gain of +10
Non-inverting op-amp gain is given by
![Gain=V_{out} /V_{in} =1 + R_{f}/R_{in}](https://tex.z-dn.net/?f=Gain%3DV_%7Bout%7D%20%2FV_%7Bin%7D%20%20%3D1%20%2B%20R_%7Bf%7D%2FR_%7Bin%7D)
![10=1+(10k/R_{in})](https://tex.z-dn.net/?f=10%3D1%2B%2810k%2FR_%7Bin%7D%29)
![10-1=10k/R_{in}](https://tex.z-dn.net/?f=10-1%3D10k%2FR_%7Bin%7D)
![9=10k/R_{in}](https://tex.z-dn.net/?f=9%3D10k%2FR_%7Bin%7D)
![R_{in} =10k/9](https://tex.z-dn.net/?f=R_%7Bin%7D%20%3D10k%2F9)
Ω
For Gain of +1
To get a Gain of +1, make
which results in
∞
The output is directly connected to the input which makes
equal to
Therefore, giving a gain of exactly 1.
![V_{out} =G*V_{in}](https://tex.z-dn.net/?f=V_%7Bout%7D%20%3DG%2AV_%7Bin%7D)
![G=1](https://tex.z-dn.net/?f=G%3D1)
This kind of design configuration is also known as Voltage Follower.
Negative feedback is being used to design these op-amp amplifiers.
![\frac{V_{out}}{V_{in}} =\frac{G}{1+\beta G}](https://tex.z-dn.net/?f=%5Cfrac%7BV_%7Bout%7D%7D%7BV_%7Bin%7D%7D%20%20%3D%5Cfrac%7BG%7D%7B1%2B%5Cbeta%20G%7D)
Negative feedback increases the stability at the cost of reduced gain.
The gain is reduced by a factor of
Negative feedback reduces noise and distortion and improves frequency response of the amplifier.
An ideal op-amp should have infinite input resistance and zero output resistance. Negative feedback increases the input impedance and reduces the output impedance.
too much sun is dangerous for humans and can cause cancer so it's important that light is reflected for example a pool reflects water back to space that is why water sometimes is cold because it reflects light