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Question Number 134323 by aurpeyz last updated on 02/Mar/21

A lens is required to have a power of −2.5 dioptres in air. the convex front surface has a radius of curvature of 30cm. calculate the radius of curvature of the rear surface

$${A}\:{lens}\:{is}\:{required}\:{to}\:{have}\:{a}\:{power}\:{of} \\ $$$$−\mathrm{2}.\mathrm{5}\:{dioptres}\:{in}\:{air}.\:{the}\:{convex} \\ $$$${front}\:{surface}\:{has}\:{a}\:{radius}\:{of}\:{curvature} \\ $$$${of}\:\mathrm{30}{cm}.\:{calculate}\:{the}\:{radius}\:{of}\:{curvature} \\ $$$${of}\:{the}\:{rear}\:{surface} \\ $$

Answered by ajfour last updated on 02/Mar/21

(1/f)=(μ−1)((1/R_1 )−(1/R_2 )) −(5/2)=(1/2)(((100)/(30))−((100)/R_2 )) ⇒ ((100)/R_2 )=5+((100)/(30)) = ((25)/3) R_2 =12cm

$$\frac{\mathrm{1}}{{f}}=\left(\mu−\mathrm{1}\right)\left(\frac{\mathrm{1}}{{R}_{\mathrm{1}} }−\frac{\mathrm{1}}{{R}_{\mathrm{2}} }\right) \\ $$$$−\frac{\mathrm{5}}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{100}}{\mathrm{30}}−\frac{\mathrm{100}}{{R}_{\mathrm{2}} }\right) \\ $$$$\Rightarrow\:\:\frac{\mathrm{100}}{{R}_{\mathrm{2}} }=\mathrm{5}+\frac{\mathrm{100}}{\mathrm{30}}\:=\:\frac{\mathrm{25}}{\mathrm{3}} \\ $$$${R}_{\mathrm{2}} =\mathrm{12}{cm} \\ $$

Commented by aurpeyz last updated on 02/Mar/21

appreciated thanks

$${appreciated}\:{thanks} \\ $$

Commented by aurpeyz last updated on 02/Mar/21

what is the value of μ?

$${what}\:{is}\:{the}\:{value}\:{of}\:\mu? \\ $$

Commented by ajfour last updated on 02/Mar/21

refractive index of lens(glass) with respect to that of the medium surrounding the lens (here air).

$${refractive}\:{index}\:{of}\:{lens}\left({glass}\right) \\ $$$${with}\:{respect}\:{to}\:{that}\:{of}\:{the} \\ $$$${medium}\:{surrounding}\:{the}\:{lens} \\ $$$$\left({here}\:{air}\right). \\ $$

Commented by ajfour last updated on 02/Mar/21

different glasses may have different values of refractive index, if not given in quwstion (such as yours) we take it to be μ_(glass) =1.5 , μ_(air) =1

$${different}\:{glasses}\:{may}\:{have} \\ $$$${different}\:{values}\:{of}\:{refractive} \\ $$$${index},\:{if}\:{not}\:{given}\:{in}\:{quwstion} \\ $$$$\left({such}\:{as}\:{yours}\right)\:{we}\:{take}\:{it}\:{to}\:{be} \\ $$$$\mu_{{glass}} =\mathrm{1}.\mathrm{5}\:\:,\:\mu_{{air}} =\mathrm{1} \\ $$

Commented by aurpeyz last updated on 02/Mar/21

you changed 1 to 100 in line 2

$${you}\:{changed}\:\mathrm{1}\:{to}\:\mathrm{100}\:{in}\:{line}\:\mathrm{2} \\ $$

Commented by ajfour last updated on 02/Mar/21

Power in dioptres is obtained from P=(1/f) only when f is in metres. So i converted took R_1 =((30)/(100))m

$${Power}\:{in}\:{dioptres}\:{is}\:{obtained} \\ $$$${from}\:{P}=\frac{\mathrm{1}}{{f}}\:\:{only}\:{when} \\ $$$${f}\:{is}\:{in}\:{metres}.\:{So}\:{i}\:{converted} \\ $$$${took}\:\:{R}_{\mathrm{1}} =\frac{\mathrm{30}}{\mathrm{100}}{m}\:\: \\ $$

Commented by aurpeyz last updated on 02/Mar/21

thanks so much. i appreciate alot

$${thanks}\:{so}\:{much}.\:{i}\:{appreciate}\:{alot} \\ $$

Commented by aurpeyz last updated on 02/Mar/21

thanks so much. i appreciate alot

$${thanks}\:{so}\:{much}.\:{i}\:{appreciate}\:{alot} \\ $$

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