Find the number.
between theme is:
i-50°
ii-60°
iii-45°
iv-30°
v-90°

Number of images formed by two plane surfaces inclined at an angle θ depends upon the value of n, where n is evaluated as n = [tex]\dfrac{360 \degree}{\theta} [/tex].

Now

Case :- 1 If n is even then number of images formed = n - 1

Case :- 2 If n is odd then number of images formed is n

Case :- 3 If n is in fractions, then number of images formed is the integral part of the fraction.

Let's solve the problem now!!

[tex]\large\underline{\sf{Solution-i}}[/tex]

[tex]\tt \: \theta \: = \: 50 \degree \\ [/tex]

So,

[tex]\tt \: n = \: \dfrac{360\degree }{50\degree } \\ [/tex]

[tex]\tt \: n = \: \dfrac{36 }{5} \\ [/tex]

[tex]\tt \: n = \: 7\dfrac{1}{5} \\ [/tex]

[tex]\tt\implies \:\boxed{ \rm{ \:Number \: of \: images \: = \: 7 \: }} \\ [/tex]

[tex]\large\underline{\sf{Solution-ii}}[/tex]

[tex]\tt\: \theta \: = 60\degree \\ [/tex]

So,

[tex]\tt \: n = \: \dfrac{360\degree }{60\degree } \\ [/tex]

[tex]\rm \: n = 6\\ [/tex]

So,

[tex]\tt\implies \:\boxed{ \rm{ \:Number \: of \: images \: = \: 6 - 1 = 5\: }} \\ [/tex]

[tex]\large\underline{\sf{Solution-iii}}[/tex]

[tex]\tt \: \theta \: = 45\degree \\ [/tex]

So,

[tex]n = \: \dfrac{360\degree }{45\degree } \\[/tex]

[tex]\tt \: n \: = \: 8 \\ [/tex]

Thus,

[tex]\tt\implies \:\boxed{ \tt{ \:Number \: of \: images \: = \: 8 - 1\: = 7 }} \\ [/tex]

[tex]\large\underline{\sf{Solution-iv}}[/tex]

[tex]\tt \: \theta \: = 30\degree \\ [/tex]

So,

[tex]\tt \: n = \: \dfrac{360\degree }{30\degree } \\[/tex]

[tex]\tt \: n = 12 \\ [/tex]

Thus,

[tex]\tt\implies \:\boxed{ \rm{ \:Number \: of \: images \: = \: 12 - 1 = 11 \: }} \\ [/tex]

[tex]\large\underline{\sf{Solution-v}}[/tex]

[tex]\tt \: \theta \: = 90\degree \\ [/tex]

So,

[tex]\tt \: n = \: \dfrac{360\degree }{90\degree } \\[/tex]

[tex]\tt\: n \: = \: 4 \\ [/tex]

Thus,

[tex]\tt\implies \:\boxed{ \tt{ \:Number \: of \: images \: = \: 4 - 1 = 3\: }} \\ [/tex]

#CarryOnLearning

[tex]\qquad\qquad\qquad\qquad\qquad\qquad\tt{fri \: 03-04-2022} \\ \qquad\qquad\qquad\qquad\qquad\qquad\tt{11:27 \: am}[/tex]