Question

an object 5 cm in length is placed at a distance of 20cm in front of concave mirror of radius of curvature 30cm.Find the position of the image‚ its nature and size.​

Answer 1

Explanation:

Radius of curvature (R) = 30 cm

f = R/2 = 30/2 = 15 cm

u = -20 cm,

h= 5 cm.

1/v +1/u = 1/f

1/v = 1/f – 1/u

1/v = 1/15 – 1/-20

v = 8. 57 cm

Image is virtual and erect and formed behind the mirror.

m = -v/u

m = hi/ho

hi/5= 8.57/20

= 0.428

hi = 0.428 x 5 = 2.14cm

Position of Image: Behind the mirror.

Nature of Image: Virtual and Erect.

Size of the Image: Diminished.

Answer 2

$\begin{lgathered}\begin{gathered}\sf \blue{\underline{ Question:-}}\\\\\end{gathered}\end{lgathered}$

5. The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram.

$\begin{lgathered}\begin{gathered}\\\\\sf \red{\underline{Given:-}}\\\\\end{gathered}\end{lgathered}$

The measures of two adjacent angles of a parallelogram are in the ratio 3:2.

$\begin{lgathered}\begin{gathered}\\\\\sf \large \red{\underline{To \: Find:-}}\\\\\end{gathered}\end{lgathered}$

Find the measure of each of the angles of the parallelogram.

$\begin{lgathered}\begin{gathered}\\\\\sf \large \red{\underline{Solution :- }}\\\\\end{gathered}\end{lgathered}$

$\text{ \sf suppose the angles be equal to 3x and 2x}$

$\boxed{ \sf \orange{ we \: have \: ardjacent \: angles \: of \: a \: parallelogram \: = 180}}$

$\begin{lgathered}\begin{gathered}\\ \sf \underline{ \green{putting \: all \: values : }}\end{gathered}\end{lgathered}$

$\begin{lgathered}\begin{gathered}\: \\ \sf \to \: 3x + 2 x = 180\: \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \:5x = 180 \\ \\ \: \sf \to \: \: \: \: \: \: \: \: \: \: \:x \: = \frac{180}{5} \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \:x \: = \cancel{ \frac{180}{5} } \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \purple{x = 36}\\\\\end{gathered}\end{lgathered}$

$\begin{lgathered}\begin{gathered}\sf \to \: 3x \\ \sf \to \: 3 \times 36 \\ \sf \to \red{108 }\\ \\ \\ \sf \to \: 2x \\ \sf \to \: 2 \times 36 \\ \sf \to \orange{72} \\\end{gathered}\end{lgathered}$

$\sf \large\underline{ \blue{verification }} \huge \dag$

$\begin{lgathered}\begin{gathered}\\ \\ \sf \to 3x + 2x = 180 \\ \\ \sf \to \: 3 \times 36 +2 \times 36 = 180 \\ \\ \sf \to \: 108 + 72 = 180 \\ \\ \sf \to \:180 = 180 \\ \\ \large \underline{ \pink{ \sf \: hence \: verified}} \huge \dag\end{gathered}\end{lgathered}$