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By M.H. Freeman, PhD, MPhil, BSc, MInstP, and C.C. Hull, PhD, DIC, MInstp, CPhys (Auth.)
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Example text
The images formed by plane refracting surfaces are therefore more complicated than images formed by plane reflecting surfaces. 11, the equation for refraction at a single surface may be written: n sin i ¼ n0 sin i 0 ð2:6Þ The mathematical expression sine (normally shortened to sin) has a nonlinear relationship to the angle. 8 shows what this means. If the value of sin i had a linear relationship to i, a straight line could be drawn so that any value of i such as i1 could then be projected up to the line and the value of sin i1 read off, using the straight line.
So n20 ¼ 1 if the plate is in air. 8 Refracting prisms 41 The line B0 A0 C is parallel to the line BA1G and so the distance BB0 is equal to A1A01 because they too are parallel, being aligned with normals to the plate surfaces. Thus, the longitudinal object to image shift due to a parallel plate of index n and thickness t is along a normal to the plate and given by: 1 Image shift ¼ t 1 À ð2:14Þ n no matter where the object is behind the plate. 13. This, however, is the laterally displaced image because the plate is effectively tilted through an angle equal to i1.
1 Imaging by reflection When we look at a plane reflecting surface, such as an ordinary mirror we see – apparently behind the mirror – images of objects which are in front of the mirror. Some of the light from each object point is reflected at the mirror surface and enters the eye as though it is coming from a point behind the mirror. These nonexistent points behind the reflecting surface form images which are called virtual images. We can see them but we cannot get to them. The light from the original object is diverging and continues to diverge after reflection at the plane surface.