! A lensball is a simple physical system: a sphere of glass of refractive index $n=1.5$ and of radius $R=5\;cm$.
! A lensball is a simple physical system: a sphere of glass of refractive index $`n=1.5`$ and of radius $R=5\;cm$.
!
! A ball lensball is placed in front of a painting. Depending on the position of the observer or the camera, the optical system (the sequence of simple optical elements crossed by light between the physical object and the observed image) that forms the image differs.
! * The optical axis is oriented positively in the direction of light propagation (from the painting towards the lensball).
!
! * The first spherical refracting surface $DS1$ encountered by the light has the follwing characteristics :<br>
! $\overline{S_1C_1}=+|R|=+5\;cm$ , $n_{ini}=1$ and $n_{fin}=1.5$
! * The first spherical refracting surface $`DS1`$ encountered by the light has the follwing characteristics :<br>
! $`\overline{S_1C_1}=+|R|=+5\;cm`$ , $`n_{ini}=1`$ and $`n_{fin}=1.5`$
!
! * The second spherical refracting surface $DS2$ encountered by the light has the follwing characteristics :<br>
! $\overline{S_2C_2}=-|R|=-5\;cm$ , $n_{ini}=1.5$ and $n_{fin}=1$
! $`\overline{S_2C_2}=-|R|=-5\;cm`$ , $`n_{ini}=1.5`$ and $`n_{fin}=1`$
!
! * Algebraic distance between $DS1$ and $DS2$ is : $\overline{S_1S_2}=+10\;cm$
! * Algebraic distance between $DS1$ and $DS2$ is : $`\overline{S_1S_2}=+10\;cm`$
! </details>
! <detailsmarkdown=1>
! <summary>
! If you had to determine the characteristics of the image (position, size), how would you handle the problem?
! </summary>
! * $DS1$ gives an image $B_1$ of an object $B$. This image $B_1$ for $DS1$ becomes the object for $DS2$. $DS2$ gives an image $B'1$ of the object $B_1$
! * $`DS1`$ gives an image $`B_1`$ of an object $`B`$. This image $`B_1`$ for $`DS1`$ becomes the object for $`DS2`$. $`DS2`$ gives an image $`B'1`$ of the object $`B_1`$
! What are the two optical systems at the origin of the two images of the painting? And can you characterize each of the single optical elements (+ their relative distances) that make up each of these optical systems ?
! </summary>
! * A first optical system $OS1$ is composed of a simple convexe spherical mirror (the object is reflected on the front face of the ball lensball). Keaping the ioptical axis positively oriented in the direction of the incident light propagation on the lensball, the algebraic value of the mirror radius is : $\overline{SC}=+5\;cm$.
! * The second optical system $OS2$ is composed of three simple optical elements :<br><br>
! 1) The light crosses a spherical refracting surface $DS1$ with characteristics : $\overline{S_1C_1}=+|R|=+5\;cm$ , $n_{ini}=1$ and $n_{fin}=1.5$.<br><br>
! 2) Then the light is reflected at the surface of the last lensball interface that acts like a spherical mirror of characteristics : $\overline{S_2C_2}=-|R|=-5\;cm$, $n=1.5$.<br><br>
! 3) Finally the light crosses back the first interface of the lensball that acts like a spherical refracting surface those characteristics are : $\overline{S_3C_3}=+|R|=+5\;cm$ , $n_{ini}=1.5$ and $n_{fin}=1$.<br><br>
! Relative algebraic distances between the different elements of $OS2$ are :<br>
! $\overline{S_1S_2}=+10\;cm$ and $\overline{S_2S_3}=-10\;cm$
! * A first optical system $`OS1`$ is composed of a simple convexe spherical mirror (the object is reflected on the front face of the ball lensball). Keaping the ioptical axis positively oriented in the direction of the incident light propagation on the lensball, the algebraic value of the mirror radius is : $\overline{SC}=+5\;cm$.
! * The second optical system $`OS2`$ is composed of three simple optical elements :<br><br>
! 1) The light crosses a spherical refracting surface $`DS1`$ with characteristics : $`\overline{S_1C_1}=+|R|=+5\;cm`$ , $`n_{ini}=1`$ and $`n_{fin}=1.5`$.<br><br>
! 2) Then the light is reflected at the surface of the last lensball interface that acts like a spherical mirror of characteristics : $`\overline{S_2C_2}=-|R|=-5\;cm`$, $`n=1.5`$.<br><br>
! 3) Finally the light crosses back the first interface of the lensball that acts like a spherical refracting surface those characteristics are : $`\overline{S_3C_3}=+|R|=+5\;cm`$ , $`n_{ini}=1.5$ and $n_{fin}=1`$.<br><br>
! Relative algebraic distances between the different elements of $`OS2`$ are :<br>
! $`\overline{S_1S_2}=+10\;cm`$ and $`\overline{S_2S_3}=-10\;cm`$
