diff options
| -rw-r--r-- | coupling_angles.m | 96 |
1 files changed, 82 insertions, 14 deletions
diff --git a/coupling_angles.m b/coupling_angles.m index 3af9c87..df7c5f1 100644 --- a/coupling_angles.m +++ b/coupling_angles.m @@ -1,12 +1,15 @@ %% Calculates incident angle for proper coupling into the disc via prism % angle of the prism faces in degrees -prism_angle=45; +prism_angle_in_degrees = 45; + +prism_angle = prism_angle_in_degrees*pi/180; %% prism index of refraction % Rutile (TiO2) see http://refractiveindex.info/?group=CRYSTALS&material=TiO2 n_rutile_o = 2.4885; n_rutile_e = 2.75324; + n_p=n_rutile_o %% disk material index of refraction @@ -24,13 +27,20 @@ theta_p=asin(n_d/n_p); theta_p_in_degrees=theta_p*180/pi %% now lets see what angle it does with other face of the prism -theta_p_in_degrees_2=-(theta_p_in_degrees-prism_angle) - -%% now we calculate refracted angle out of the prism into the air -theta_air=asin(n_p*sin(theta_p_in_degrees_2/180*pi)); +theta_p_2=(prism_angle - theta_p); +theta_p_in_degrees_2=theta_p_2*180/pi + +%% now we calculate refracted angle out of the prism into the air with respect to the normal +% positive means above the normal +asin_arg=n_p*sin(theta_p_2); +if (abs(asin_arg)>1) error('quiting: at the right prism face we experienced total internal reflection'); end +theta_air=asin(asin_arg); % convert to degrees theta_air_in_degrees=theta_air*180/pi +%% angle in the air relative to horizon +theta_air_rlh=(theta_air+prism_angle); +theta_air_rlh_in_degrees=theta_air_rlh*180/pi %% Lets make a picture % 1st face of the prism lays at y=0 and spans from x=-1 to x=1 @@ -38,10 +48,10 @@ x_face_1=linspace(-1,1); y_face_1=0*x_face_1; % 2nd face to the right of origin and at angle prism_angle with respect to negative x direction x_face_2=linspace(1,0); -y_face_2=(1-x_face_2)*tan(prism_angle/180*pi); +y_face_2=(1-x_face_2)*tan(prism_angle); % 3rd face to the left of origin and at angle prism_angle with respect to negative x direction x_face_3=linspace(-1,0); -y_face_3=(x_face_3+1)*tan(prism_angle/180*pi); +y_face_3=(x_face_3+1)*tan(prism_angle); %% draw prism figure(1); hold off; @@ -49,7 +59,7 @@ plot(x_face_1, y_face_1, 'k-', x_face_2, y_face_2, 'k-', x_face_3, y_face_3, 'k- hold on %% disk center will be located in point (0,-R); -R=.5 +R=.25; dc_x=0; dc_y=-R; x_disk=dc_x+R*cos(linspace(0,2*pi)); y_disk=dc_y+R*sin(linspace(0,2*pi)); @@ -58,22 +68,80 @@ plot(x_disk,y_disk,'k-') %% beam trace inside the prism % crossing of the beam with 1st (right) face of the prism -% we are solving cot(theta_p)*x=cot(prism_angle)*(1-x) -x_cross_1=cot(prism_angle/180*pi)/(cot(prism_angle/180*pi)+cot(theta_p)); +% we are solving cot(theta_p)*x=tan(prism_angle)*(1-x) +x_cross_1=tan(prism_angle)/(tan(prism_angle)+cot(theta_p)); +y_cross_1=x_cross_1*cot(theta_p); x_beam_prism_1=linspace(0,x_cross_1); -y_beam_prism_1=linspace(0,x_cross_1)*cot(theta_p); +y_beam_prism_1=x_beam_prism_1*cot(theta_p); plot(x_beam_prism_1, y_beam_prism_1, 'r-'); %% beam out of prism x_out_strt=x_cross_1; y_out_strt=x_cross_1*cot(theta_p); -% angle in the air relative to horizon -theta_air_rlh=(theta_air_in_degrees-prism_angle)/180*pi; if (abs(theta_air_rlh)<pi/2) x_out_stop=1; else x_out_stop=0; end x_out_1=linspace(x_out_strt, x_out_stop); y_out_1=y_out_strt+tan(theta_air_rlh)*(x_out_1-x_out_strt); plot(x_out_1, y_out_1, 'r-'); +%% draw normal at the point of 1st face intercection +theta_norm_rlh=pi/2-prism_angle; +% coordinates of normal outside the prism +x_norm_out=linspace(x_cross_1,1); +y_norm_out=y_cross_1+(x_norm_out-x_cross_1)*tan(theta_norm_rlh); + +% coordinates of normal inside the prism +y_norm_in=linspace(y_cross_1,0); +x_norm_in=x_cross_1+(y_norm_in-y_cross_1)*tan(theta_norm_rlh+pi); +plot(x_norm_out, y_norm_out, 'b-', x_norm_in, y_norm_in, 'b-'); + +%% arc to show theta_air +R_arc=.1; +phi_arc=linspace(theta_air_rlh,theta_norm_rlh); +x_arc_air=x_cross_1+R_arc*cos(phi_arc); +y_arc_air=y_cross_1+R_arc*sin(phi_arc); +plot(x_arc_air, y_arc_air, 'b-'); +%% annotation theta_air_in_degrees +str=sprintf('theta_{a}=%.1f',theta_air_in_degrees); +str=strcat('\',str,'^{o}'); +text(x_arc_air(end)+.05,y_arc_air(end), str); + +%% normal at the disk contact +y_norm_in=linspace(0.,0.5); +x_norm_in=y_norm_in*0; +plot(x_norm_in, y_norm_in, 'b-'); + +%% arc to show theta_p +R_arc=.1; +phi_arc=linspace(pi/2-theta_p,pi/2); +x_arc_prism=R_arc*cos(phi_arc); +y_arc_prism=R_arc*sin(phi_arc); +plot(x_arc_prism, y_arc_prism, 'b-'); +%% annotation theta_air_in_degrees +str=sprintf('theta_{p}=%.1f',theta_p_in_degrees); +str=strcat('\',str,'^{o}'); +text(x_arc_prism(1)+0.05, y_arc_prism(1), str); + +%% arc to show theta_p_2 +R_arc=.1; +phi_arc=linspace(theta_norm_rlh+theta_p_2+pi,theta_norm_rlh+pi); +x_arc_prism_2=x_cross_1+R_arc*cos(phi_arc); +y_arc_prism_2=y_cross_1+R_arc*sin(phi_arc); +plot(x_arc_prism_2, y_arc_prism_2, 'b-'); +%% annotation theta_air_in_degrees +str=sprintf('theta_{p2}=%.1f',theta_p_in_degrees_2); +str=strcat('\',str,'^{o}'); +text(x_arc_prism_2(1)+.05,y_arc_prism_2(1), str); + + +str=sprintf('n_d=%.3f',n_d); +text(0,1.1, str); + +str=sprintf('n_p=%.3f',n_p); +text(0,1.2, str); + % force same aspect ratio for axis -axis('square'); +axis([-1,1,-0.5,1.5],'equal'); + +%% output of the plot to the file +print('prism_disk_coupling.pdf'); |