Question
Derive lens Maker formula $\frac{1}{f}=\left(n_{21}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$. Here are the general meanings of the symbols used in the formula. Draw necessary diagram.
✓
Answer
This formula relates the focal length of a lens to the refractive index of its material and the radii of curvature of its two surfaces.
$\frac{1}{f}=\left(n_{21}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$,where $n_{21}$ is the refractive index,$R_1$ and $R_2$ are radii of curvature.
It is derived by considering refraction at two spherical surfaces and applying the formula $\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$$\frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R}$ for each surface.
$\frac{1}{f}=\left(n_{21}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$,where $n_{21}$ is the refractive index,$R_1$ and $R_2$ are radii of curvature.
It is derived by considering refraction at two spherical surfaces and applying the formula $\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$$\frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R}$ for each surface.
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In the year 1939, German scientist Otto Hahn and Strassmann discovered that when an uranium isotope was bombarded with a neutron, it breaks into two intermediate mass fragments. It was observed that, the sum of the masses of new fragments formed were less than the mass of the original nuclei. This difference in the mass appeared as the energy released in the process. Thus, the phenomenon of splitting of a heavy nucleus (usually A > 230) into two or more lighter nuclei by the bombardment of proton, neutron $\alpha$-particle, etc. with liberation of energy is called nuclear fission.
$\ _{92}\text{U}^{235}+\ _0\text{n}^{1}\rightarrow_{92}\text{U}^{236} \rightarrow\ _{56}\text{B}^{114}+\ _{36}\text{Kr}^{89}\ +3\ _{0}\text{n}^{1} + \text{Q}$
$\big[\because \ _{92}\text{U}^{236}= \text{Unstable nucleus}\big]$
→$\ _{92}\text{U}^{235}+\ _0\text{n}^{1}\rightarrow_{92}\text{U}^{236} \rightarrow\ _{56}\text{B}^{114}+\ _{36}\text{Kr}^{89}\ +3\ _{0}\text{n}^{1} + \text{Q}$
$\big[\because \ _{92}\text{U}^{236}= \text{Unstable nucleus}\big]$
- Nuclear fission can be explained on the basis of.
- Millikan's oil drop method
- Liquid drop model
- Shell model
- Bohr's model.
- For sustaining the nuclear fission chain reaction in a sample (of small size) of $_{92}^{235}\text{U}$ it is desirable to slow down fast neutrons by.
- Friction
- Elastic damping/ scattering
- Absorption
- None of these.
- Which of the following is/ are fission reaction(s)?
- $_0^1\text{n}\ +\ _{92}^{235}\text{U}\rightarrow\ _{92}^{235}\text{U}\rightarrow\ _{51}^{133}\text{Sb}+\ _{41}^{99}\text{nb}+\ 4_1^0\text{n}$
- $_0^1\text{n}\ +\ _{92}^{235}\text{U}\rightarrow\ _{54}^{1.40}\text{Xe}+\ _{38}^{94}\text{Sr}\ +2_0^1\text{n}$
- $_1^2\text{H}\ +\ _1^2\text{H}\rightarrow\ _2^3\text{He}+\ _0^1\text{n}$
- Both II and III
- Both I and III
- Only II
- Both I and II
- On an average, the number of neutrons and the energy of a neutron released per fission of a uranium atom are respectively.
- 2.5 and 2 keV
- 3 and 1 keV
- 2.5 and 2 MeV
- 2 and 2 keV
- In any fission process, ratio of mass of daughter nucleus to mass of parent nucleus is.
- Less than I
- Greater than I
- Equal to I
- Depends o the mass of parent nucleus.
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