Fresnel equation derivation
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When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
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In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
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When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
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Exercise:
Derive the Fresnel reflection and transmission formulas for s-polarized electric field E perpicular to the plane plane waves incident on a surface.
Solution:
To compute the Fresnel reflection formulas we first have to consider the specific boundary conditions for this problem. itemize item The tangential electric field E_parallel is continuous Rightarrow component of E that lies in the xz plane is continuous as one moves across the erface item The tangential magnetic field B_perp is continuous Rightarrow total B field in the plane of the erface is continuous. itemize This rewrites o: E_ixz+E_rxz E_txz -B_ixzcostheta_i + B_rxzcostheta_r -B_txzcostheta_t Now considering that BfracnEc and theta_itheta_r we can rewrite Eq. as n_iE_r-E_icos theta_i -n_tE_tcos theta_t now inserting Eq. n_iE_r-E_icos theta_i -n_tE_r+E_icos theta_t. Rearranging this we have: E_rn_icostheta_i+n_tcostheta_t E_in_icostheta_i-n_tcostheta_t Solving for fracE_rE_i yields the reflection coefficient: r_perp fracE_rE_i fracn_icostheta_i-n_tcostheta_tn_icostheta_i+n_tcostheta_t analogously the transmission coefficient is t_perp fracE_tE_i fracn_icostheta_in_icostheta_i+n_tcostheta_t
Derive the Fresnel reflection and transmission formulas for s-polarized electric field E perpicular to the plane plane waves incident on a surface.
Solution:
To compute the Fresnel reflection formulas we first have to consider the specific boundary conditions for this problem. itemize item The tangential electric field E_parallel is continuous Rightarrow component of E that lies in the xz plane is continuous as one moves across the erface item The tangential magnetic field B_perp is continuous Rightarrow total B field in the plane of the erface is continuous. itemize This rewrites o: E_ixz+E_rxz E_txz -B_ixzcostheta_i + B_rxzcostheta_r -B_txzcostheta_t Now considering that BfracnEc and theta_itheta_r we can rewrite Eq. as n_iE_r-E_icos theta_i -n_tE_tcos theta_t now inserting Eq. n_iE_r-E_icos theta_i -n_tE_r+E_icos theta_t. Rearranging this we have: E_rn_icostheta_i+n_tcostheta_t E_in_icostheta_i-n_tcostheta_t Solving for fracE_rE_i yields the reflection coefficient: r_perp fracE_rE_i fracn_icostheta_i-n_tcostheta_tn_icostheta_i+n_tcostheta_t analogously the transmission coefficient is t_perp fracE_tE_i fracn_icostheta_in_icostheta_i+n_tcostheta_t
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Exercise:
Derive the Fresnel reflection and transmission formulas for s-polarized electric field E perpicular to the plane plane waves incident on a surface.
Solution:
To compute the Fresnel reflection formulas we first have to consider the specific boundary conditions for this problem. itemize item The tangential electric field E_parallel is continuous Rightarrow component of E that lies in the xz plane is continuous as one moves across the erface item The tangential magnetic field B_perp is continuous Rightarrow total B field in the plane of the erface is continuous. itemize This rewrites o: E_ixz+E_rxz E_txz -B_ixzcostheta_i + B_rxzcostheta_r -B_txzcostheta_t Now considering that BfracnEc and theta_itheta_r we can rewrite Eq. as n_iE_r-E_icos theta_i -n_tE_tcos theta_t now inserting Eq. n_iE_r-E_icos theta_i -n_tE_r+E_icos theta_t. Rearranging this we have: E_rn_icostheta_i+n_tcostheta_t E_in_icostheta_i-n_tcostheta_t Solving for fracE_rE_i yields the reflection coefficient: r_perp fracE_rE_i fracn_icostheta_i-n_tcostheta_tn_icostheta_i+n_tcostheta_t analogously the transmission coefficient is t_perp fracE_tE_i fracn_icostheta_in_icostheta_i+n_tcostheta_t
Derive the Fresnel reflection and transmission formulas for s-polarized electric field E perpicular to the plane plane waves incident on a surface.
Solution:
To compute the Fresnel reflection formulas we first have to consider the specific boundary conditions for this problem. itemize item The tangential electric field E_parallel is continuous Rightarrow component of E that lies in the xz plane is continuous as one moves across the erface item The tangential magnetic field B_perp is continuous Rightarrow total B field in the plane of the erface is continuous. itemize This rewrites o: E_ixz+E_rxz E_txz -B_ixzcostheta_i + B_rxzcostheta_r -B_txzcostheta_t Now considering that BfracnEc and theta_itheta_r we can rewrite Eq. as n_iE_r-E_icos theta_i -n_tE_tcos theta_t now inserting Eq. n_iE_r-E_icos theta_i -n_tE_r+E_icos theta_t. Rearranging this we have: E_rn_icostheta_i+n_tcostheta_t E_in_icostheta_i-n_tcostheta_t Solving for fracE_rE_i yields the reflection coefficient: r_perp fracE_rE_i fracn_icostheta_i-n_tcostheta_tn_icostheta_i+n_tcostheta_t analogously the transmission coefficient is t_perp fracE_tE_i fracn_icostheta_in_icostheta_i+n_tcostheta_t
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