Light: Mirrors and Lenses – Formula & Equation Sheet
Essential formulas and equations from Curiosity, tailored for Class 8 in Science.
This one-pager compiles key formulas and equations from the Light: Mirrors and Lenses chapter of Curiosity. 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
i = r
i is the angle of incidence, and r is the angle of reflection. This formula expresses the law of reflection, stating that the angle at which light strikes a reflective surface is equal to the angle at which it reflects. It is foundational in optics.
f = (R / 2)
f is the focal length, and R is the radius of curvature of the mirror. This formula shows that the focal length of a spherical mirror is half of its radius of curvature. Useful for understanding mirror behavior.
1/f = 1/v + 1/u
f is focal length, v is the image distance, and u is the object distance in lenses and mirrors. This lens/mirror formula relates object distance, image distance, and focal length, crucial for image formation calculations.
M = h'/h
M is the magnification, h' is the height of the image, and h is the height of the object. This helps determine how much larger or smaller an image is compared to the object.
tan(θ) = h / d
θ is the angle, h is the height of the object, and d is the distance from the object to the mirror. This formula aids in calculating angles of reflection based on object height and distance.
C = 2πr
C is the circumference, and r is the radius of the mirror or lens. Understanding the circumference can be helpful in experiments involving circular mirrors.
n = c / v
n is the refractive index, c is the speed of light in vacuum, and v is the speed of light in the medium. This describes how light propagates differently in various media, impacting lens functions.
P = 1/f
P is the power of the lens in diopters (D), and f is the focal length in meters. This formula is important for identifying the strength of the lens; positive for converging lenses and negative for diverging.
sin(i) / sin(r) = v / u
This equation states that the ratio of the sines of the angles of incidence and refraction is constant. It forms the basis of Snell's Law, important in understanding light behavior at media boundaries.
PV = nRT
In some scenarios, this equation relates pressure (P), volume (V), the number of moles (n), the universal gas constant (R), and temperature (T). Relevant for understanding light behavior in gases adjacent to mirrors and lenses.
Equations
i + r = 90°
The sum of the angles of incidence and reflection with respect to the normal is always 90 degrees. This concept is essential when analyzing reflective surfaces.
R = 2f
R is the radius of curvature, and f is the focal length. This relationship is fundamental in optics when dealing with spherical mirrors.
M = -v/u
Magnification (M) can also be expressed as the negative of the image distance (v) divided by the object distance (u). This allows for determining image orientation in relation to the object.
f = (n-1)(R / n)
This relates the focal length of a lens to its radius of curvature (R) and refractive index (n). Important for lens design and understanding light passage.
v = u + 2f
For images formed by spherical mirrors, this equation relates the image distance (v) to the object distance (u) and the focal length (f). It describes position relations for object-image systems.
P = 1/f = n - 1
Relating power, focal length, and lens behavior, this equation helps in predicting how strong a lens will be based on its properties.
D = 1/f(meters)
Power (P) in diopters is inversely related to the focal length in meters. This definition is useful for differentiating between lens types based on their focusing capabilities.
n1 * sin(θ1) = n2 * sin(θ2)
This equation is used to calculate the angle of refraction when light passes between two media of different densities, directly applicable in lens applications.
v = f * T
In wave optics, v is wave speed, f is frequency, and T is wavelength. While not directly in the mirrors/lenses chapter, it's fundamental when exploring light properties.
h' = h * M
The height of the image (h') can be calculated by multiplying the object's height (h) by the magnification (M). This provides a direct method for concluding image dimensions based on object size.
