Introduction
Ray optics, also known as geometrical optics, is the branch of physics that describes light propagation in terms of rays. The primary principles of ray optics include reflection, refraction, and the formation of images by lenses and mirrors. This study note will also cover optical instruments like microscopes and telescopes, which are essential topics for the NEET Physics exam.
Basic Concepts of Ray Optics
Nature of Light
Light is an electromagnetic wave that can be approximated as rays when dealing with objects much larger than its wavelength. These rays travel in straight lines and obey the laws of reflection and refraction.
Reflection of Light
Reflection occurs when light bounces off a surface. The laws of reflection are:
- The angle of incidence ($i$) is equal to the angle of reflection ($r$).
- The incident ray, the reflected ray, and the normal to the surface all lie in the same plane.
$$ i = r $$
NoteThe angle of incidence and the angle of reflection are measured with respect to the normal to the surface.
Refraction of Light
Refraction is the bending of light as it passes from one medium to another with a different refractive index. The laws of refraction (Snell's Law) are:
- The incident ray, the refracted ray, and the normal to the interface of two media lie in the same plane.
- The ratio of the sine of the angle of incidence ($i$) to the sine of the angle of refraction ($r$) is constant and is equal to the refractive index ($n$) of the second medium relative to the first.
$$ n_1 \sin i = n_2 \sin r $$
TipRemember that light bends towards the normal when it enters a denser medium and away from the normal when it enters a less dense medium.
Total Internal Reflection
Total internal reflection occurs when light attempts to move from a denser medium to a less dense medium at an angle greater than the critical angle ($\theta_c$). The critical angle is given by:
$$ \sin \theta_c = \frac{n_2}{n_1} $$
where $n_1$ is the refractive index of the denser medium and $n_2$ is the refractive index of the less dense medium.
ExampleFor example, the critical angle for light traveling from water ($n_1 = 1.33$) to air ($n_2 = 1.00$) is: $$ \theta_c = \sin^{-1} \left( \frac{1}{1.33} \right) \approx 48.75^\circ $$
Image Formation by Mirrors
Plane Mirrors
- The image formed by a plane mirror is virtual, erect, and of the same size as the object.
- The distance of the image from the mirror is equal to the distance of the object from the mirror.
Spherical Mirrors
Spherical mirrors can be concave or convex.
Concave Mirrors
- Principal Axis: The line passing through the center of curvature ($C$) and the pole ($P$).
- Focal Point ($F$): The point where parallel rays converge after reflection.
- Focal Length ($f$): The distance between the pole and the focal point. For concave mirrors, $f = \frac{R}{2}$, where $R$ is the radius of curvature.
The mirror equation and magnification are given by:
$$ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} $$ $$ m = \frac{h_i}{h_o} = -\frac{v}{u} $$
where $u$ is the object distance, $v$ is the image distance, $h_o$ is the object height, and $h_i$ is the image height.
Convex Mirrors
- The focal point is virtual and located behind the mirror.
- The mirror equation and magnification remain the same.
Do not confuse the sign conventions for concave and convex mirrors. For concave mirrors, the focal length is negative, while for convex mirrors, it is positive.
Image Formation by Lenses
Convex Lenses
- Principal Axis: The line passing through the centers of curvature of the lens surfaces.
- Focal Point ($F$): The point where parallel rays converge after refraction.
- Focal Length ($f$): The distance between the center of the lens and the focal point.
The lens formula and magnification are given by:
$$ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} $$ $$ m = \frac{h_i}{h_o} = \frac{v}{u} $$
Concave Lenses
- The focal point is virtual and located on the same side as the object.
- The lens formula and magnification remain the same.
For lenses, the focal length is positive for convex lenses and negative for concave lenses.
Optical Instruments
Microscope
A microscope uses two lenses to magnify small objects. It consists of an objective lens and an eyepiece.
- Objective Lens: Forms a real, inverted, and magnified image of the object.
- Eyepiece: Acts as a magnifying glass to further enlarge the image formed by the objective lens.
The total magnification ($M$) is the product of the magnifications of the objective ($M_o$) and the eyepiece ($M_e$):
$$ M = M_o \times M_e $$
Telescope
A telescope is used to view distant objects and also consists of an objective lens and an eyepiece.
- Objective Lens: Forms a real, inverted, and diminished image of the distant object.
- Eyepiece: Magnifies the image formed by the objective lens.
The magnifying power ($M$) of a telescope is given by:
$$ M = \frac{f_o}{f_e} $$
where $f_o$ is the focal length of the objective lens and $f_e$ is the focal length of the eyepiece.
ExampleFor example, if a telescope has an objective lens with a focal length of 1000 mm and an eyepiece with a focal length of 25 mm, the magnifying power is: $$ M = \frac{1000}{25} = 40 $$
Conclusion
Ray optics and optical instruments are fundamental topics in NEET Physics. Understanding the principles of reflection, refraction, and image formation by mirrors and lenses is crucial. Additionally, optical instruments like microscopes and telescopes have significant applications in scientific research and everyday life. Mastery of these concepts will not only help in exams but also provide a strong foundation for further studies in optics and related fields.
