Post on 22-Jan-2020
transcript
The prism:
The Apex angle of a prism is Φ. We derive in class the above prism equation.
The light is refracted when entering and when leaving the prism. The minimum angle of deviation is δmin. It occurs when the incidence angle θ1 is such that the refracted ray inside makes the same angle with the normal to the two prism faces as shown in the above Figure.
Knowing apex angle Φ and measuring the deviation angle δmin , one can determine the refractive index n.
(see your Lab 1). A hollow prism filled with liquid can be used to determine n of the liquid.
n =sin ! +"min
2!
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sin !2!
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Image forma0on for mirrors:
Object O is at object distance o.
Reflected rays appear to originate at point I behind the mirror. I is called the image and i image distance.
Image forma0on -‐ geomtrically: Up to four rays can be used to construct the image geometrically – they are called the principal rays. There are of course infinitely many rays that one could use – all one has to do is to apply the law of reflec<on correctly. But the four principal rays go through special points on the mirror or op<cal axis.
For concave mirrors they are:
Image forma0on -‐ geometrically: Up to four rays can be used to construct the image geometrically – they are called the principal rays. The principal rays are the same as for concave mirrors: parallel ray, ray through centre (vertex), through focal point (F) and through C (middle of circle).
For convex mirrors they are:
The lens equa0on:
1o+1i=2R=1f
In class we derive the mirror equation:
The equation connects object distance o, image distance i and focal length f. The focal length f is the distance from the mirror on the optical axis where the image is formed for parallel rays (o= ) coming in: 1o+1i=1!+1i=1i=1f!"! f = i
!
The magnification M
is defined as
Note sign convention for M, i and o !
M =imageheightobject !height
=h 'h= !
io!
For spherical mirrors this happens at f=R/2.
The near-‐axis or pararaxial approxima0on h, δ << i, o, R:
The mirror equation we derived is derived strictly using simple geometric identities and uses an important simplification h<<R (more specifically h,δ << o, i, R). This means that the distance of the point where the optic is struck by the ray to the optical axis is small compared to the curvature radius of the mirror. This is referred to as the paraxial or near-axis approximation. This also means that α, β, γ << 1 rad and often requires that the apertures of mirrors (or lenses) are small.
If rays are impinging on the optic further away from the optical axis, nothing changes in the physics – just the geometric approximations do not hold any longer and therefore the equations become much more complex.
Reflective optics - mirrors The sign conventions are important to memorize and to apply correctly.
The sign conventions for mirrors:
• > 0 : real object (in front of lens)
• o < 0 : virtual object (behind lens)
i > 0 : real image (behind lens - note that real image for mirrors is in front of mirror)
i < 0 : virtual image (in front of lens – behind for mirror!)
M > 0 : image upright (M>1: magnified)
M < 0 : image inverted (0<M<1: demagnified)
f = R/2 > 0 : converging lens with convex surface (converging mirror with concave surface)
f = R/2 < 0 : diverging lens with concave surface (diverging mirror with convex surface)
Example:
(1) Determine image distance and magnification for
(a) o = 15 cm, f = 10 cm
(b) o = 20 cm, f = - 15 cm
(2) Draw the rays for each case.