# mirror formula for convex mirror form virtual image

All distances are measured from the pole of the mirror. Introducing Textbook Solutions. Use this online convex mirror equation calculator to find the focal length, image … Draw LN perpendicular on the principle axis. Draw LN perpendicular on the principal axis. Mirror Formula for Convex Mirror when Real Image is formed. So A’B’ is the real image of the object AB. and don’t understand the underlying physics. Terms. The image on a convex mirror is always virtual, diminished and upright. The distance between the object and the convex mirror is measured at the point where the image reflection reaches an approximate size of the object. A slide. The distances of real objects and real images are taken as positive where as that of virtual objects and virtual images are taken as negative. You can find us in almost every social media platforms. Example: The projection lens in a certain slide projector is a single thin lens. In this section, let us look at the types of images formed by a convex mirror. Get step-by-step explanations, verified by experts. Focal length and radius of curvature of a concave mirror are positive where as that of convex mirror negative. Course Hero, Inc. Object should be placed on the principal axis in the form of point object. It includes every relationship which established among the people. Let AB be an object lying on the principle axis of the convex mirror of small aperture. A slide 23.8 mm high is to be projected so that its image fills a screen 1.81. m high. \begin{align*} \text {Now} \: \Delta ‘s \: \text {NLF and A’B’F are similar, therefore} \\ \frac {A’B’}{NL} &= \frac {A’F}{NF} \dots (i) \\ \text {Since aperture of the concave mirror is small, so point N lies very close to P.} \\ NF &= PF \\ \text {Also} \\ NL &= AB \\ \text {equation} \: (i) \: \text {becomes,} \\ \frac {A’B’}{AB} &= \frac {A’F}{PF} \dots (ii) \\ \text {Also} \: \Delta ‘s \text {ABC and A’B’C are similar, therefore,} \\ \frac {A’B’}{AB} &= \frac {A’C}{AC} \dots (iii) \\ \text {From equation} \: (ii) \text {and} \: (iii), \: \text {we get} \\ \\ \frac {A’F}{PF} &= \frac {A’C}{AC} \dots (iv) \\ \text {Since all the distances are measured from the pole of the mirror, so} \\ \end{align*}, $$\left.\begin{aligned} A'F = PA' - PF \\ A'C = PC - PA' \\ AC = PA - PC\end{aligned} \right \} \dots (i)$$, \begin{align*} \text {Substituting the values of equation}\: (v)\text {in equation,}\: (iv) \text {we get} \\ \frac {PA’ – PF}{PF} &= \frac {PC – PA’}{PA - PC} \dots (vi) \\ \text {Applying sign convention,} \\ PA’ = v, PF = f, PC = R = 2f \: (\therefore R = 2f ) \\ PA &= u \\ \text {Hence equation} \: (vi) \: \text {becomes} \\ \frac {v - f}{f} &= \frac {2f – v}{u – 2f} \\ uv – 2fv – uf + 2f^2 &= 2f^2 – vt \\ uv &= uf + vf \\ \text {Dividing by uvf, we get} \\ \frac {uv}{uvf} &= \frac {uf}{uvf} + \frac {vf}{uvf} \\ \frac 1f &= \frac 1u + \frac 1v \\ \end{align*}, Mirror Formula for Concave Mirror when Virtual Image is formed. https://www.merospark.com/.../mirror-formula-for-concave-and-convex-mirror To derive mirror formula assumptions and sign conventions are made. \begin{align*} \text {Now} \: \Delta ‘s \:\text {NLF and A’B’F are similar, therefore} \\ \frac {A’B’}{NL} &= \frac {A’F}{NF} \dots (i) \\ \text {Since aperture of the concave mirror is small, so point N lies very close to P.} \\ \therefore NF = PF \: \text {and} NL = AB \\ \text {Also} \: \Delta ‘s \text {ABC and A’B’C are similar, therefore,} \\ \frac {A’B’}{AB} &= \frac {A’C}{AC}= \frac {PA’ + PC} {PC –PA}\dots (iii) \\ \end{align*}, \begin{align*} \text {From equation} \: (ii) \text {and} \: (iii), \: \text {we get} \\ \frac {PA’ + PF}{PF} &= \frac {PA’ + PC}{PC - PA} \dots (iv) \\ \text {From equation} \: (ii) \: \text {and} \: (iii), \text {we get} \\ \text {Applying sign convention} \\ PA’ = - v, PF = f, PC = R = 2f \: (\because R = 2f, PA = u) \\ \therefore \: \text {Equation} \: (iv) \: \text {becomes} \\ \frac {-v + f}{f} &= \frac {– v - 2f}{ 2f - u} \\ \text {or,} \: -2vf +uv + 2f^2 – uf &= -vf + 2f^2 \\ \text {or,} \: uv &= uf + vf \\ \end{align*}, \begin{align*} \text {Dividing by uvf, we get} \\ \frac {uv}{uvf} &= \frac {uf}{uvf} + \frac {vf}{uvf} \\ \frac 1f &= \frac 1u + \frac 1v \\ \end{align*}. A’B’ is the virtual image of the object lying behind the convex mirror as shown in the figure. Image Formation By Convex Mirror. To derive the formula following assumptions and sign conventions are made. A ray of light BL after reflecting from the concave mirror passes through the principal axis at F and goes along LB’. Privacy Convex mirrors only form virtual images Mirror equation use R 0 or f0 o Concave, The projection lens in a certain slide projector is a single thin lens. Draw LN perpendicular on the principal axis. 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