Question

$\rm\underline{Question}: -$

$\tt\red{Find \: the\:image \: distance \: for \: a \: Convex \: mirror \:} \\ \tt\red{having \: focal \: length \: 5cm, \: if \: the \: object} \\\tt\red{is \: placed \: 7cm \: from \: the \: pole \: of \: the \: mirror.}$
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Answer 1

Answer:

Height of object, ho=5cm, object distance u=−30cm, focal length f=−20cm 

Now, from mirror formula :f1=v1+u1

v1=f1−u1

      =20−1+301

      =−601

v=−60cm - image distance 

Magnification, m=−uv=−−30−60=−2

Size of image, hi=m(ho)=−2(5)=−10 cm

Answer 2

$\huge \sf\orange{\underline{ \underline{solution}: - }} \\ \\ \huge \tt \underline{given} \\ \\ \huge\tt\red{u = 7cm} \\ \\ \huge \tt \red{f = 5cm} \\ \\ \tt \green{now} \\ \\ \tt \blue{\frac{1}{v} + \frac{1}{u} = \frac{1}{f} } \\ \\ \tt \color{blue} \frac{1}{v} + \frac{1}{ - 7} = \frac{1}{5} \\ \\ \tt \color{blue} \frac{1}{v} - \frac{1}{7} = \frac{1}{5} \\ \\ \tt \color{blue} \frac{1}{v} = \frac{1}{5} + \frac{1}{7} \\ \\ \tt \color{blue} \frac{1}{v} = \frac{7 + 5}{35} \\ \\ \tt \color{blue} \frac{1}{v} = \frac{12}{35} \\ \\ \tt \color{green}v = \frac{35}{12} \: = \: 2.91 \bar6 \: \: \: \: answer$