Thin lens equation and microscope - Revision history

Mol: /* Theory */

2021-08-11T18:14:48Z

Theory

← Older revision		Revision as of 21:14, 11 August 2021
Line 11:		Line 11:
	&= \frac1{f_2} - \frac1{L-i_1} \\		&= \frac1{f_2} - \frac1{L-i_1} \\
	&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{o_1 - f_1}} \\		&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{o_1 - f_1}} \\
	~~%&= \frac1{f_2} - \frac1{ \frac{L(o_1-f_1)}{o_1-f_1}-\frac{f_1 o_1}{o_1 - f_1}} \\~~
	&= \frac1{f_2} - \frac{o_1-f_1}{ L(o_1-f_1)- f_1 o_1} \\		&= \frac1{f_2} - \frac{o_1-f_1}{ L(o_1-f_1)- f_1 o_1} \\
	\end{align}</math>		\end{align}</math>

	Magnification (for the thin lens) is <math>m = - \frac io = - \frac{i_2}{o_1}</math>.		Magnification (for the thin lens) is <math>m = - \frac io = - \frac{i_2}{o_1}</math>.

2021-08-11T18:13:10Z

Theory

← Older revision		Revision as of 21:13, 11 August 2021
Line 11:		Line 11:
	&= \frac1{f_2} - \frac1{L-i_1} \\		&= \frac1{f_2} - \frac1{L-i_1} \\
	&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{o_1 - f_1}} \\		&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{o_1 - f_1}} \\
	&= \frac1{f_2} - \frac1{ \frac{L(o_1-f_1)}{o_1-f_1}-\frac{f_1 o_1}{o_1 - f_1}} \\		%&= \frac1{f_2} - \frac1{ \frac{L(o_1-f_1)}{o_1-f_1}-\frac{f_1 o_1}{o_1 - f_1}} \\
	&= \frac1{f_2} - \frac{o_1-f_1}~~{ \frac~~{L(o_1-f_1)- f_1 o_1} \\		&= \frac1{f_2} - \frac{o_1-f_1}{ L(o_1-f_1)- f_1 o_1} \\
	\end{align}</math>		\end{align}</math>

	Magnification (for the thin lens) is <math>m = - \frac io = - \frac{i_2}{o_1}</math>.		Magnification (for the thin lens) is <math>m = - \frac io = - \frac{i_2}{o_1}</math>.

2021-08-11T18:12:45Z

Theory

← Older revision		Revision as of 21:12, 11 August 2021
Line 11:		Line 11:
	&= \frac1{f_2} - \frac1{L-i_1} \\		&= \frac1{f_2} - \frac1{L-i_1} \\
	&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{o_1 - f_1}} \\		&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{o_1 - f_1}} \\
	%&= \frac1{f_2} - \frac1{ \frac{L(o_1-f_1)}{o_1-f_1}-\frac{f_1 o_1}{o_1 - f_1}} \\		&= \frac1{f_2} - \frac1{ \frac{L(o_1-f_1)}{o_1-f_1}-\frac{f_1 o_1}{o_1 - f_1}} \\
	&= \frac1{f_2} - \frac{o_1-f_1}{ \frac{L(o_1-f_1)- f_1 o_1} \\		&= \frac1{f_2} - \frac{o_1-f_1}{ \frac{L(o_1-f_1)- f_1 o_1} \\
	\end{align}</math>		\end{align}</math>

	Magnification (for the thin lens) is <math>m = - \frac io = - \frac{i_2}{o_1}</math>.		Magnification (for the thin lens) is <math>m = - \frac io = - \frac{i_2}{o_1}</math>.

2021-08-11T18:12:34Z

Theory

← Older revision		Revision as of 21:12, 11 August 2021
Line 11:		Line 11:
	&= \frac1{f_2} - \frac1{L-i_1} \\		&= \frac1{f_2} - \frac1{L-i_1} \\
	&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{o_1 - f_1}} \\		&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{o_1 - f_1}} \\
	&= \frac1{f_2} - \frac1{ \frac{L(o_1-f_1)}{o_1-f_1}-\frac{f_1 o_1}{o_1 - f_1}} \\		%&= \frac1{f_2} - \frac1{ \frac{L(o_1-f_1)}{o_1-f_1}-\frac{f_1 o_1}{o_1 - f_1}} \\
	&= \frac1{f_2} - \frac{o_1-f_1}{ \frac{L(o_1-f_1)- f_1 o_1} } \\		&= \frac1{f_2} - \frac{o_1-f_1}{ \frac{L(o_1-f_1)- f_1 o_1} \\
	\end{align}</math>		\end{align}</math>

	Magnification (for the thin lens) is <math>m = - \frac io = - \frac{i_2}{o_1}</math>.		Magnification (for the thin lens) is <math>m = - \frac io = - \frac{i_2}{o_1}</math>.

2021-08-11T18:12:17Z

Theory

← Older revision		Revision as of 21:12, 11 August 2021
Line 11:		Line 11:
	&= \frac1{f_2} - \frac1{L-i_1} \\		&= \frac1{f_2} - \frac1{L-i_1} \\
	&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{o_1 - f_1}} \\		&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{o_1 - f_1}} \\
	%&= \frac1{f_2} - \frac1{ \frac{L(o_1-f_1)}{o_1-f_1}-\frac{f_1 o_1}{o_1 - f_1}} \\		&= \frac1{f_2} - \frac1{ \frac{L(o_1-f_1)}{o_1-f_1}-\frac{f_1 o_1}{o_1 - f_1}} \\
	&= \frac1{f_2} - \frac{o_1-f_1}{ \frac{L(o_1-f_1)- f_1 o_1} } \\		&= \frac1{f_2} - \frac{o_1-f_1}{ \frac{L(o_1-f_1)- f_1 o_1} } \\
	\end{align}</math>		\end{align}</math>

	Magnification (for the thin lens) is <math>m = - \frac io = - \frac{i_2}{o_1}</math>.		Magnification (for the thin lens) is <math>m = - \frac io = - \frac{i_2}{o_1}</math>.

2021-08-11T18:12:06Z

Theory

← Older revision		Revision as of 21:12, 11 August 2021
Line 11:		Line 11:
	&= \frac1{f_2} - \frac1{L-i_1} \\		&= \frac1{f_2} - \frac1{L-i_1} \\
	&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{o_1 - f_1}} \\		&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{o_1 - f_1}} \\
	//&= \frac1{f_2} - \frac1{ \frac{L(o_1-f_1)}{o_1-f_1}-\frac{f_1 o_1}{o_1 - f_1}} \\		%&= \frac1{f_2} - \frac1{ \frac{L(o_1-f_1)}{o_1-f_1}-\frac{f_1 o_1}{o_1 - f_1}} \\
	&= \frac1{f_2} - \~~frac1~~{ \frac{L(o_1-f_1)- f_1 o_1~~}{o_1 - f_1~~}} \\		&= \frac1{f_2} - \frac{o_1-f_1}{ \frac{L(o_1-f_1)- f_1 o_1} } \\
	\end{align}</math>		\end{align}</math>

	Magnification (for the thin lens) is <math>m = - \frac io = - \frac{i_2}{o_1}</math>.		Magnification (for the thin lens) is <math>m = - \frac io = - \frac{i_2}{o_1}</math>.

2021-08-11T18:11:29Z

Theory

← Older revision		Revision as of 21:11, 11 August 2021
Line 11:		Line 11:
	&= \frac1{f_2} - \frac1{L-i_1} \\		&= \frac1{f_2} - \frac1{L-i_1} \\
	&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{o_1 - f_1}} \\		&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{o_1 - f_1}} \\
			//&= \frac1{f_2} - \frac1{ \frac{L(o_1-f_1)}{o_1-f_1}-\frac{f_1 o_1}{o_1 - f_1}} \\
			&= \frac1{f_2} - \frac1{ \frac{L(o_1-f_1)- f_1 o_1}{o_1 - f_1}} \\
	\end{align}</math>		\end{align}</math>

	Magnification (for the thin lens) is <math>m = - \frac io = - \frac{i_2}{o_1}</math>.		Magnification (for the thin lens) is <math>m = - \frac io = - \frac{i_2}{o_1}</math>.

2021-08-11T17:24:25Z

Theory

← Older revision		Revision as of 20:24, 11 August 2021
Line 13:		Line 13:
	\end{align}</math>		\end{align}</math>

	Magnification (for the thin lens) is <math>m = - \frac io</math>.		Magnification (for the thin lens) is <math>m = - \frac io = - \frac{i_2}{o_1}</math>.

2021-08-11T17:23:25Z

Theory

← Older revision		Revision as of 20:23, 11 August 2021
Line 10:		Line 10:
	\frac1{i_2} &= \frac1{f_2} - \frac1{o_2} \\		\frac1{i_2} &= \frac1{f_2} - \frac1{o_2} \\
	&= \frac1{f_2} - \frac1{L-i_1} \\		&= \frac1{f_2} - \frac1{L-i_1} \\
	&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{f_1 ~~+ o_1~~}} \\		&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{o_1 - f_1}} \\
	\end{align}</math>		\end{align}</math>

	Magnification (for the thin lens) is <math>m = - \frac io</math>.		Magnification (for the thin lens) is <math>m = - \frac io</math>.

2021-08-11T17:22:49Z

Theory

← Older revision		Revision as of 20:22, 11 August 2021
Line 10:		Line 10:
	\frac1{i_2} &= \frac1{f_2} - \frac1{o_2} \\		\frac1{i_2} &= \frac1{f_2} - \frac1{o_2} \\
	&= \frac1{f_2} - \frac1{L-i_1} \\		&= \frac1{f_2} - \frac1{L-i_1} \\
	&= \frac1{f_2} - \frac1{L-~~(i_1)~~} \\		&= \frac1{f_2} - \frac1{L-\frac{f_1 o_1}{f_1 + o_1}} \\
	\end{align}</math>		\end{align}</math>

	Magnification (for the thin lens) is <math>m = - \frac io</math>.		Magnification (for the thin lens) is <math>m = - \frac io</math>.