This chapter explores the behavior of light through ray optics, focusing on reflection and refraction. It is essential for understanding optical instruments and the functioning of the human eye.
RAY OPTICS AND OPTICAL INSTRUMENTS – Formula & Equation Sheet
Essential formulas and equations from Physics Part - II, tailored for Class 12 in Physics.
This one-pager compiles key formulas and equations from the RAY OPTICS AND OPTICAL INSTRUMENTS chapter of Physics Part - II. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
f = R/2
f is the focal length (in meters) of a spherical mirror, and R is the radius of curvature (in meters). This formula relates the focal length of the mirror to its radius of curvature, indicating that the focal length is half the radius.
1/f = 1/v + 1/u
f is the focal length, v is the image distance, and u is the object distance (both measured from the mirror/lens). This mirror equation is fundamental for calculating image positions.
m = -v/u
m is the magnification, v is the image distance, and u is the object distance. This formula helps to determine the size and orientation of the image relative to the object.
n = sin(i)/sin(r)
n is the refractive index, i is the angle of incidence, and r is the angle of refraction. This equation (Snell’s law) defines how light bends when passing between different media.
n1/n2 = sin(r2)/sin(r1)
n1 and n2 are the refractive indices of the two media, r1 is the angle of refraction in medium 1, and r2 is the angle of refraction in medium 2. This formula relates the angles of incidence and refraction to the refractive indices of the two media.
D = n - 1
D is the deviation in a thin prism; n is the refractive index of the prism material. This is used to determine how much light bends when passing through the prism.
P = 1/f
P is the power of the lens in diopters (D), and f is the focal length in meters. This formula expresses how the converging or diverging effect of a lens can be quantified.
1/f = 1/f1 + 1/f2 + ...
f is the effective focal length of a system of thin lenses in contact, f1, f2 are the focal lengths of individual lenses. This shows how to combine multiple lenses.
m_total = m_obj * m_eye
m_total is the total magnification of a microscope, m_obj is the magnification from the objective lens, and m_eye is the magnification from the eyepiece. This formula helps design microscopes for desired magnification.
D_m = 2i - A
D_m is the angle of minimum deviation in a prism, i is the angle of incidence, and A is the prism angle. This formula describes how light behaves in a prism at its minimum deviation.
Equations
sin(i_c) = n_2/n_1
i_c is the critical angle for total internal reflection, n_2 is the refractive index of the rarer medium, and n_1 is the refractive index of the denser medium. This equation determines the critical angle above which light will not pass into the second medium.
D = (n-1)A
D is the angle of deviation, n is the refractive index of the prism, and A is the apex angle of the prism. This relation helps in understanding how light is deviated by a prism.
v = u * (n1/n2)
v is the velocity of light in a medium, and u is the velocity of light in vacuum. This relationship shows how light speed changes as it enters different media.
1/v = 1/u + 1/f
This is another form of the lens maker's formula, where v is the image distance, u is the object distance, and f is the focal length. This form is helpful in analyzing both convex and concave lenses.
m = h'/h = v/u
m is the linear magnification, h' is the height of the image, h is the height of the object, v is the image distance, and u is the object distance. This shows how to relate image height and object height with their respective distances.
f = (R1*R2)/(n2-n1)
This is the lens maker's equation for choosing lens parameters based on radii of curvature R1, R2 and refractive index differences n1, n2. It helps in designing lenses.
tan(θ) = opposite/adjacent
This basic trigonometric function relates the angles involved in light refraction and reflection scenarios, allowing for the understanding of angles in ray diagrams.
v = c/n
v is the speed of light in a medium, c is the speed of light in vacuum, and n is the refractive index of the medium. This highlights how the medium affects light speed.
f = (R/2) for spherical mirrors
R is the radius of curvature. This equation simplifies analysis of mirror shapes and focuses for practical applications.
m = 1 + D/f for microscopes
Where D is the near point distance (typically 25 cm). It is used to optimize magnification for small lenses in biological or material examination.
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