Respuesta :
Your question is missing one part as "magnification"
i have completed the missing part below
Answer:
a. [tex]d_{i}=-0.0566cm[/tex]
b. [tex]M=441.69[/tex]
Explanation:
For this type of numerical we will use the following formulas
[tex]\frac{n1}{d_{o} }+\frac{n_{2} }{d_{i} }=\frac{n_{2}-n_{1} }{R}[/tex]......... Eq1
where,
[tex]n_{1}[/tex][tex]=[/tex]refractive index of the medium surrounding refracting surface/object
i.e. [tex]n_{1}[/tex]=[tex]n_{air}[/tex]
[tex]n_{2}[/tex][tex]=[/tex] refractive index of the refracting surface/object
i.e. [tex]n_{2}=n_{glass}[/tex]
[tex]d_{0}=[/tex] distance of object from the vertex of the refracting surface
[tex]d_{i}=[/tex]distance of image from the vertex of the refracting surface
[tex]R=[/tex]radius of curvature of the refracting surface
[tex]M=\frac{d_{0} }{d_{i} }[/tex] ........... Eq2
where,
[tex]M=[/tex]magnification
Convention:
[tex]R>0\for\ the\ convex\ refractive\ surface\ of\ curvature\\\ R<0\ for\ the\ concave\ refractive\ surface\ of\ curvature[/tex]
Given:
[tex]n_{1}[/tex]=[tex]n_{air}[/tex][tex]=1.0[/tex]
[tex]n_{2}=n_{glass}[/tex][tex]=1.5[/tex]
[tex]d_{0}=[/tex][tex]25cm[/tex]
[tex]R=-11[/tex][tex]cm[/tex] because refraction surface is concave
Required:
a. [tex]d_{i}=[/tex][tex]?[/tex]
b. [tex]M=?[/tex]
Solution:
a. putting values in eq1, we get
[tex]\frac{1.0}{25}+\frac{1.5}{d_{i} }=\frac{1.5-1.0}{-11}[/tex]
[tex]\frac{1.5}{d_{i} }=-0.045-0.040[/tex]
[tex]d_{i}=(-0.085)(\frac{1}{1.5} )[/tex]
[tex]d_{i}=-0.0566[/tex]cm
b. [tex]M=\frac{25}{-0.05665}[/tex]
[tex]M=441.69[/tex]
