Reflection of Light — Revision Notes

⚡ 30-Second Revision

Laws of Reflection:

* $\theta_i = \theta_r$ * Incident ray, reflected ray, normal are coplanar.

Plane Mirror: — Virtual, erect, laterally inverted, same size, $u = |v|$.
Mirror Rotation (fixed incident ray): — Reflected ray rotates by $2\theta$.
Number of Images (two mirrors at $\theta$): — $n = \frac{360^\circ}{\theta} - 1$ (if even or symmetric odd), $n = \frac{360^\circ}{\theta}$ (if asymmetric odd), $n = \text{floor}(\frac{360^\circ}{\theta})$ (if fraction).
Spherical Mirrors: — Concave (converging, $f<0$), Convex (diverging, $f>0$).
Focal Length: — $f = R/2$.
Mirror Formula: — $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ (with New Cartesian Sign Convention).
Magnification: — $m = \frac{h_i}{h_o} = -\frac{v}{u}$.

* $m>0$: Erect, Virtual. * $m<0$: Inverted, Real. * $|m|>1$: Magnified; $|m|<1$: Diminished; $|m|=1$: Same size.

2-Minute Revision

Reflection of light is the bouncing back of light from a surface. It follows two laws: the angle of incidence equals the angle of reflection, and the incident ray, reflected ray, and normal all lie in the same plane.

Surfaces can cause specular reflection (smooth, clear images) or diffuse reflection (rough, scattered light). Plane mirrors form virtual, erect, laterally inverted images of the same size and distance.

If a plane mirror rotates by $\theta$, the reflected ray rotates by $2\theta$. Spherical mirrors are either concave (converging, negative focal length) or convex (diverging, positive focal length). The focal length ($f$) is half the radius of curvature ($R$), i.

e., $f=R/2$. The mirror formula, $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$, is used to find image distance ($v$) given object distance ($u$) and focal length ($f$). Always use the New Cartesian Sign Convention consistently.

Magnification ($m = -v/u = h_i/h_o$) tells you the image size and orientation: positive $m$ means erect/virtual, negative $m$ means inverted/real. Convex mirrors always form virtual, erect, and diminished images.

5-Minute Revision

Reflection is the phenomenon where light bounces back into the same medium. The two laws of reflection are fundamental: the angle of incidence ($heta_i$) equals the angle of reflection ($heta_r$), and the incident ray, reflected ray, and normal are coplanar.

Remember to always measure angles with respect to the normal, not the surface. Specular reflection occurs on smooth surfaces like mirrors, producing clear images, while diffuse reflection from rough surfaces scatters light, making objects visible from all angles.

For plane mirrors, images are always virtual, erect, laterally inverted, and the same size as the object. The image distance equals the object distance ($|u|=|v|$). A key concept is mirror rotation: if a plane mirror rotates by an angle $\theta$ (incident ray fixed), the reflected ray rotates by $2\theta$ in the same direction.

The number of images formed by two inclined plane mirrors at angle $\theta$ is $n = \frac{360^\circ}{\theta} - 1$ (if $\frac{360^\circ}{\theta}$ is an integer) or $n = \text{floor}(\frac{360^\circ}{\theta})$ (if fractional).

Spherical mirrors are either concave (converging, $f<0$) or convex (diverging, $f>0$). The focal length ($f$) is half the radius of curvature ($R$), i.e., $f=R/2$. The New Cartesian Sign Convention is critical: pole as origin, incident light from left to right, distances in incident direction positive, opposite negative, above principal axis positive, below negative.

For a real object, $u$ is always negative. For concave mirrors, $f$ and $R$ are negative; for convex mirrors, they are positive. The mirror formula is $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$. Linear magnification $m = \frac{h_i}{h_o} = -\frac{v}{u}$ determines image size and orientation.

If $m>0$, the image is erect and virtual. If $m<0$, it's inverted and real. $|m|>1$ means magnified, $|m|<1$ means diminished. Convex mirrors always form virtual, erect, and diminished images. Concave mirrors can form both real and virtual images depending on object position.

Practice numerical problems rigorously, paying close attention to sign conventions.

Prelims Revision Notes

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Laws of Reflection:

* Angle of incidence ($heta_i$) = Angle of reflection ($heta_r$). * Incident ray, reflected ray, and normal lie in the same plane. * Angles are always measured with respect to the normal.

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Types of Reflection:

* Specular (Regular): From smooth surfaces (e.g., mirrors). Parallel rays reflect parallel. Forms clear images. * Diffuse (Irregular): From rough surfaces (e.g., paper). Parallel rays scatter. Makes objects visible from all angles.

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Plane Mirrors:

* Image is Virtual, Erect, Laterally Inverted. * Image size = Object size ($h_i = h_o$). * Image distance = Object distance ($|v| = |u|$). * Rotation: If mirror rotates by $\theta$ (incident ray fixed), reflected ray rotates by $2\theta$ in the same direction.

* **Number of Images (two mirrors at $\theta$):** * If $\frac{360^\circ}{\theta}$ is even integer: $n = \frac{360^\circ}{\theta} - 1$. * If $\frac{360^\circ}{\theta}$ is odd integer: $n = \frac{360^\circ}{\theta} - 1$ (symmetric object), $n = \frac{360^\circ}{\theta}$ (asymmetric object).

* If $\frac{360^\circ}{\theta}$ is fraction: $n = \text{floor}(\frac{360^\circ}{\theta})$.

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Spherical Mirrors (Concave & Convex):

* Pole (P): Center of mirror surface. * Center of Curvature (C): Center of sphere mirror is part of. * Radius of Curvature (R): Distance PC. * Principal Axis: Line through P and C. * Principal Focus (F): Point where parallel rays converge (concave) or appear to diverge from (convex) after reflection. * Focal Length (f): Distance PF. $f = R/2$.

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New Cartesian Sign Convention:

* Pole is origin. * Incident light from left to right. * Distances in incident direction (+), opposite (-). * Heights above principal axis (+), below (-). * Real object: $u$ is always negative. * Concave mirror: $f < 0$, $R < 0$. * Convex mirror: $f > 0$, $R > 0$.

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Mirror Formula: — $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$.

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Linear Magnification (m):

* $m = \frac{h_i}{h_o} = -\frac{v}{u}$. * $m > 0$: Image Erect, Virtual. * $m < 0$: Image Inverted, Real. * $|m| > 1$: Magnified; $|m| < 1$: Diminished; $|m| = 1$: Same size.

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Image Characteristics by Spherical Mirrors:

* Concave Mirror: Forms both real/virtual, inverted/erect, magnified/diminished images depending on object position. * Convex Mirror: Always forms Virtual, Erect, Diminished images for real objects.

Vyyuha Quick Recall

For mirror formula signs, remember 'U-V-F': Usually Unique (object is always real, so $u$ is negative). Very Variable (image $v$ can be positive or negative). Fixed For Form (focal length $f$ is negative for concave, positive for convex).