JEE main and advanced Tips for Geometrical Optics

In this blog post we will study JEE main and advanced Tips for Geometrical Optics

Geometrical Optics

The study of images produced by either refraction or by reflection of light it’s called geometrical optics. This area of study deals with the trajectories of beams of light, not taking into account the effects of light has a wave, like when interference occurs. This effects can be negligible when the wave length is very small in comparison with the objects that the light encounters in it’s path.

To study the position of an image with respect to an object we utilize this definitions:

  • Optic axis: abscissa axis perpendicular to the refractory plain. The positive sense is the right side of the         refractory plain, which is the sense of advance of the light.
  • Object space: it’s the space that is situated to the left of the diopter.
  • Image space: it’s the space that is situated to the right of the diopter.
  • Real and virtual image: Despite the fictional character of an image, we say an image is real as long as it’s formed by two convergent refractory light beams. A real image must be observed in a screen. We said it’s a virtual image if we take it by the prolongations of two divergent refractory beams.

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Two interesting subjects of the optical axis are the object focus and the image focus:

  • Object focus: Point F of the optical axis at which it’s image it’s located in the infinity of the image space.
  • Image focus: Point F’ of the optical axis which is the image of a point in infinity of the object space.
  • The construction of images is very simple if the principal rays are used:
  • Parallel ray: beam of light that is parallel to the optic axis which goes from the outermost top of the object. After refracting, this ray goes through the image focus.
  • Focal ray: beam of light that goes through the top of the object and also through the object focus, which results in it being refracted in a parallel way. After refracting, this ray goes through the image focus, like the parallel ray.
  • Radial ray: beam of light that goes through the top of the object and is directed to the center of curvature of the diopter. This ray does not refract and continues in the same direction, because it’s incidence angle is equal to zero.

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Straight or non curved mirrors

Mirrors are extremely polished surfaces with a reflective capacity of 95% (or greater) of the intensity of the incident light.

Let us consider a beam of light that is refracted from a medium of index n to other hypothetical index of refraction n’. Applying Snell’s law:

n . sin(ai) = n’ . sin(ar)

From this law, we deduce that ai = -ar. A negative refraction angle means that the direction of the light beam was inverted, so the beam bounces back.

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In a plain mirror, the positions x and x’ of an object and their image are related: x = x’

The image is virtual, since it’s formed with the prolongations of light beams.

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Optical instruments

The drawing of ray in lenses and mirrors systems is particularly important to the design of the following optical instruments:

a) The microscope:

a microscope is a lens system that produces an enlarged virtual image from a tiny little object. The most simpler microscope is a convergent lens, the magnifying glass. He object is placed between the lens and the focus, in a way that the image is virtual and it’s at a distance that the it’s the same distance as the minimum distance for a sharp, clear vision, around 25 cm.

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The composed microscope consists in two convergent lenses which have little focal distance, called objective and ocular. The focal distance of the objective f, is far smaller than the focal distance f’ of the ocular. The object AB is placed at a slight greater distance from the objective that the point f. The objective forms a first image, a’b’, that acts as an object for the ocular. The image a’b’ must be at a distance of the ocular that is slightly smaller than f’. The final image, ab, is virtual, inverted and much more bigger than the object AB. The object AB it’s positioned in such a way that ab is at a distance from the ocular that it’s the same distance of minimum sharp vision, around 25 cm. This condition it’s achieved through focusing, which consists in moving all the microscope with respect to the object. (You can observe the image through a convex lens).

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b) The telescope:

In the telescope the object is a convergent lens of focal distance f that is really big, sometimes it’s several meters across. As the object AB is very far away, it’s image a’b’ prouced by the objective, it’s in it’s focus F0. You only need central rays to know the position of the image.

The ocular is a convergent lens of focal distance f’ that is smaller. It’s positioned in such a way that the intermediate image, a’b’, it’s between the ocular and it’s focus, and the final image ab it’s at the minimal sharp vision distance, that it’s around 25cm. The focus is achieved by moving the ocular, since the objective it’s impossible to move. (You can watch the image through a concave lens).

c) Prisms:

A prism is an object that is capable of refracting, reflecting and discomposing white light in it’s rainbow colors. Generally, this objects have the shape of a triangular prism, from there they got that name.

According to Snell’s law, when light goes from air to the prism glass, it decreases it’s velocity, diverting it’s trajectory and forming an angle with respect to the interface. As a consequence, light is refracted or reflected. The incidence angle of the beam of light and the prism and air refractory indices determine the quantity of light that will be reflected, the quantity that will be refracted or if only one of the two things will happen.

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1. Reflective prisms only reflect light, since they are easier to make than mirrors, they are used in optic instruments like binoculars, monoculars and other similar instruments.

2. Dispersive prisims are used to decompose light in the rainbow spectrum, because the refraction index depends on the frequency, the white light entering the prism is an assortment of different frequencies and each one diverts in a different way. Blue light is diminished at a slower pace that red light.

3. Polarizing prisms separate every light beam in polarizing components.

If you still have doubts about Geometrical Optics, you can read from this book.

Keep reading the blog. And prepare smartly. Best of luck !

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