Treat Each Surface as an Object for the Next, and Track the Signs
Ray-optics problems with several elements are solved in order: the image formed by one element is the object for the next. Keep a sign convention, apply the lens or mirror formula at each step, and multiply the magnifications.
Lenses, Plane Mirrors and Refraction in Layers is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
Lens formula and combinations
For a thin lens, 1/v - 1/u = 1/f, with distances measured from the lens and taken positive in the direction of the incident light, and the magnification is m = v/u.
If a plane mirror stands 20 cm behind the lens, it intercepts the converging rays 10 cm before they would meet; those rays act as a virtual object 10 cm behind the mirror. A plane mirror forms an image at an equal distance on the other side of its plane, so the real final image appears 10 cm in front of the mirror, which is 10 cm from the lens, and the total magnification is -2.
Refraction through layers and apparent depth
Seen from air, a layer of thickness t and refractive index μ appears to have thickness t/μ.
For an observer inside one medium, use the relative refractive index of the other medium to the observer's medium: viewed from the water, the glass appears 9 x (4/3)/(3/2) = 8 cm thick, so the total is 8 + 8 = 16 cm; viewed from the glass, the water appears 8 x (3/2)/(4/3) = 9 cm thick and the total is 18 cm.
Two plane mirrors
A ray reflected successively by two plane mirrors inclined at θ is turned through 2(180° - θ) in total.
An image in a plane mirror is always as far behind the mirror as the object is in front, so images in an inclined mirror can be located by reflecting the object, or the point where the rays would converge, across the mirror plane.
OlympIQ exam lens
- ✓1/v - 1/u = 1/f with a consistent sign convention; m = v/u
- ✓The image from one element is the object for the next; multiply the magnifications
- ✓Rays that a mirror intercepts before they converge act as a virtual object behind the mirror
- ✓Apparent thickness from air is the sum of t/μ; inside a medium use μ_other/μ_observer
- ✓Plane-mirror image distance equals object distance, on the opposite side of the mirror
Do not measure the distance to the second element from the original object. After the lens forms an image, the mirror's object distance is measured from the mirror to that image, and an image that would lie beyond the mirror is a virtual object.
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