How is lateral displacement (reflection/refraction) derived?

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The discussion centers on the derivation of the equation for lateral displacement in light refraction, specifically S = t*sin(theta1 - theta2)/cos(theta2). The user seeks clarity on how this equation is derived, indicating a connection to Snell's Law and trigonometry. It is noted that lateral displacement occurs when light transitions from a less dense medium, like air, to a more dense medium, such as glass, and is refracted again upon exiting the slab. Key variables are defined: S represents lateral displacement, t is the slab width, theta1 is the angle of incidence, and theta2 is the angle of refraction. Understanding these concepts is essential for better comprehension and memorization of the equation.
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my book is only introductory and they only gave me the equation S = t*sin( theta1 -theta2)/cos(theta2), i like to know how its derived so i can better understand and memorize this... i know i can probably work this out myself but i don't know where to start

i am assuming it has something to do with snells law and trig, but I am bad at those
 
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Lateral displacement of what, exactly? It might help if you tell us what the the variables stand for.
 
when light goes from a less dense media to a more dense media (air to glass), it is refracted. if its a glass slab, it will be refracted again as it exits the slab. S = lateral displacement of the incidence ray. t = the width of the slab, theta 1 is the angle of incidence while theta 2 is the angle of refraction
 

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